Presentations of groups /:
The aim of this book is to provide an introduction to combinatorial group theory. Any reader who has completed first courses in linear algebra, group theory and ring theory will find this book accessible. The emphasis is on computational techniques but rigorous proofs of all theorems are supplied. T...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge, U.K. ; New York, NY, USA :
Cambridge University Press,
1997.
|
| Ausgabe: | 2nd ed. |
| Schriftenreihe: | London Mathematical Society student texts ;
15. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | The aim of this book is to provide an introduction to combinatorial group theory. Any reader who has completed first courses in linear algebra, group theory and ring theory will find this book accessible. The emphasis is on computational techniques but rigorous proofs of all theorems are supplied. This new edition has been revised throughout, including new exercises and an additional chapter on proving that certain groups are infinite. |
| Beschreibung: | 1 online resource (x, 216 pages) : illustrations |
| Bibliographie: | Includes bibliographical references (pages 201-209) and index. |
| ISBN: | 9781139168410 113916841X 9781107089037 1107089034 9781107095236 1107095239 |
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| 245 | 1 | 0 | |a Presentations of groups / |c D.L. Johnson. |
| 250 | |a 2nd ed. | ||
| 260 | |a Cambridge, U.K. ; |a New York, NY, USA : |b Cambridge University Press, |c 1997. | ||
| 300 | |a 1 online resource (x, 216 pages) : |b illustrations | ||
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| 490 | 1 | |a London Mathematical Society student texts ; |v 15 | |
| 504 | |a Includes bibliographical references (pages 201-209) and index. | ||
| 588 | 0 | |a Print version record. | |
| 520 | |a The aim of this book is to provide an introduction to combinatorial group theory. Any reader who has completed first courses in linear algebra, group theory and ring theory will find this book accessible. The emphasis is on computational techniques but rigorous proofs of all theorems are supplied. This new edition has been revised throughout, including new exercises and an additional chapter on proving that certain groups are infinite. | ||
| 505 | 0 | |a Cover; Title; Copyright; Dedication; CONTENTS; PREFACE TO THE SECOND EDITION; CHAPTER 1 FREE GROUPS; 1. Definition and elementary properties; 1.1 Definition and elementary properties; 2. Existence of F(X); 1.2 Existence of F(X); 1.3 Further properties of F(X); 3. Further properties of F(X); 1.3 Further properties of F(X); Exercises; CHAPTER 2 SCHREIER'S METHOD; 1. The well-ordering of F; 2.1 The well-ordering of F; 2. The Schreier transversal; 2.2 The Schreier transversal; 3. The Schreier generators; 4. Decomposition of the set A; 5. Freeness of the generators B; 6. Conclusion; Exercises | |
| 505 | 8 | |a CHAPTER 3 NIELSEN'S METHOD1. The finitely-generated case; 2. Example 1; 3. The general case; 4. Further applications; Exercises; CHAPTER 4 FREE PRESENTATIONS OF GROUPS; 1. Basic concepts; 2. Induced homomorphisms; 3. Direct products; 4. Tietze transformations; 5. van Kampen diagrams; Exercises; CHAPTER 5 SOME POPULAR GROUPS; 1. The quaternions; 2. The Heisenberg group; 3. Symmetric groups; 4. Semi-direct products; 5. Groups of symmetries; 6. Polynomials under substitution; 7. The rational numbers; Exercises; CHAPTER 6 FINITELY-GENERATED ABELIAN GROUPS; 1. Groups-made-abelian | |
| 505 | 8 | |a 2. Free abelian groups3. Change of generators; 4. The invariant factor theorem for matrices; 5. The basis theorem; Exercises; CHAPTER 7 FINITE GROUPS WITH FEW RELATIONS; 1. Metacyclic groups; 2. Interesting groups with three generators; 3. Cyclically-presented groups; Exercises; CHAPTER 8 COSET ENUMERATION; 1. The basic method; 2. A refinement; Exercises; CHAPTER 9 PRESENTATIONS OF SUBGROUPS; 1. The method; 2. Alternating groups; 3. Braid groups; 4. von Dyck groups; 5. Triangle groups; 6. Free products; 7. HNN-extensions; 8. The Schur multiplicator; Exercises | |
| 505 | 8 | |a CHAPTER 10 PRESENTATIONS OF GROUP ExTENSIONS1. Basic concepts; 2. The main theorem; 3. Special cases; (S) Semi-direct products; (A) Extensions with abelian kernel; (Z) Central extensions; (D) The direct product; 4. Finite p-groups; Exercises; CHAPTER 11 RELATION MODULES; 1. G-modules; 2. The augmentation ideal; 3. Derivations; 4. Free differential calculus; 5. The fundamental isomorphism; Exercises; CHAPTER 12 AN ALGORITHM FOR N/N'; 1. The Jacobian; 2. The proof; 3. Examples; Exercises; CHAPTER 13 FINITE p-GROUPS; 1. Review of elementary properties; 2. Power-commutator presentations | |
| 505 | 8 | |a 3. mod p modulesExercises; CHAPTER 14 THE NILPOTENT QUOTIENT ALGORITHM; 1. The algorithm; 2. An example; 3. An improvement; Exercises; CHAPTER 15 THE GOLOD-SHAFAREVICH THEOREM; 1. The proof; 2. An example; 3. Related results; Exercises; CHAPTER 16 PROVING SOME GROUPS INFINITE; 1. Dimension subgroups; 2. The Gaschiitz-Newman formulae; 3. Newman's criterion; 4. Fibonacci update; Exercises; Guide to the literature and references; INDEX; Dramatis Personae | |
| 650 | 0 | |a Presentations of groups (Mathematics) |0 http://id.loc.gov/authorities/subjects/sh85106447 | |
| 650 | 6 | |a Présentations de groupes (Mathématiques) | |
| 650 | 7 | |a MATHEMATICS |x Group Theory. |2 bisacsh | |
| 650 | 7 | |a Presentations of groups (Mathematics) |2 fast | |
| 650 | 7 | |a Gruppentheorie |2 gnd | |
| 650 | 7 | |a TEORIA DOS GRUPOS. |2 larpcal | |
| 650 | 7 | |a COHOMOLOGIA DE GRUPOS. |2 larpcal | |
| 650 | 7 | |a ÁLGEBRA HOMOLÓGICA. |2 larpcal | |
| 650 | 7 | |a ÁLGEBRA. |2 larpcal | |
| 758 | |i has work: |a Presentations of groups (Text) |1 https://id.oclc.org/worldcat/entity/E39PCGR4RqBxkr3bg8xVQ3K6Dm |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |a Johnson, D.L. |t Presentations of groups. |b 2nd ed. |d Cambridge, U.K. ; New York, NY, USA : Cambridge University Press, 1997 |z 0521585422 |w (DLC) 96036823 |w (OCoLC)35688069 |
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Datensatz im Suchindex
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| adam_text | |
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| author | Johnson, D. L. |
| author_facet | Johnson, D. L. |
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| author_variant | d l j dl dlj |
| building | Verbundindex |
| bvnumber | localFWS |
| callnumber-first | Q - Science |
| callnumber-label | QA174 |
| callnumber-raw | QA174 .J64 1997eb |
| callnumber-search | QA174 .J64 1997eb |
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| contents | Cover; Title; Copyright; Dedication; CONTENTS; PREFACE TO THE SECOND EDITION; CHAPTER 1 FREE GROUPS; 1. Definition and elementary properties; 1.1 Definition and elementary properties; 2. Existence of F(X); 1.2 Existence of F(X); 1.3 Further properties of F(X); 3. Further properties of F(X); 1.3 Further properties of F(X); Exercises; CHAPTER 2 SCHREIER'S METHOD; 1. The well-ordering of F; 2.1 The well-ordering of F; 2. The Schreier transversal; 2.2 The Schreier transversal; 3. The Schreier generators; 4. Decomposition of the set A; 5. Freeness of the generators B; 6. Conclusion; Exercises CHAPTER 3 NIELSEN'S METHOD1. The finitely-generated case; 2. Example 1; 3. The general case; 4. Further applications; Exercises; CHAPTER 4 FREE PRESENTATIONS OF GROUPS; 1. Basic concepts; 2. Induced homomorphisms; 3. Direct products; 4. Tietze transformations; 5. van Kampen diagrams; Exercises; CHAPTER 5 SOME POPULAR GROUPS; 1. The quaternions; 2. The Heisenberg group; 3. Symmetric groups; 4. Semi-direct products; 5. Groups of symmetries; 6. Polynomials under substitution; 7. The rational numbers; Exercises; CHAPTER 6 FINITELY-GENERATED ABELIAN GROUPS; 1. Groups-made-abelian 2. Free abelian groups3. Change of generators; 4. The invariant factor theorem for matrices; 5. The basis theorem; Exercises; CHAPTER 7 FINITE GROUPS WITH FEW RELATIONS; 1. Metacyclic groups; 2. Interesting groups with three generators; 3. Cyclically-presented groups; Exercises; CHAPTER 8 COSET ENUMERATION; 1. The basic method; 2. A refinement; Exercises; CHAPTER 9 PRESENTATIONS OF SUBGROUPS; 1. The method; 2. Alternating groups; 3. Braid groups; 4. von Dyck groups; 5. Triangle groups; 6. Free products; 7. HNN-extensions; 8. The Schur multiplicator; Exercises CHAPTER 10 PRESENTATIONS OF GROUP ExTENSIONS1. Basic concepts; 2. The main theorem; 3. Special cases; (S) Semi-direct products; (A) Extensions with abelian kernel; (Z) Central extensions; (D) The direct product; 4. Finite p-groups; Exercises; CHAPTER 11 RELATION MODULES; 1. G-modules; 2. The augmentation ideal; 3. Derivations; 4. Free differential calculus; 5. The fundamental isomorphism; Exercises; CHAPTER 12 AN ALGORITHM FOR N/N'; 1. The Jacobian; 2. The proof; 3. Examples; Exercises; CHAPTER 13 FINITE p-GROUPS; 1. Review of elementary properties; 2. Power-commutator presentations 3. mod p modulesExercises; CHAPTER 14 THE NILPOTENT QUOTIENT ALGORITHM; 1. The algorithm; 2. An example; 3. An improvement; Exercises; CHAPTER 15 THE GOLOD-SHAFAREVICH THEOREM; 1. The proof; 2. An example; 3. Related results; Exercises; CHAPTER 16 PROVING SOME GROUPS INFINITE; 1. Dimension subgroups; 2. The Gaschiitz-Newman formulae; 3. Newman's criterion; 4. Fibonacci update; Exercises; Guide to the literature and references; INDEX; Dramatis Personae |
| ctrlnum | (OCoLC)817925523 |
| dewey-full | 512/.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.2 |
| dewey-search | 512/.2 |
| dewey-sort | 3512 12 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2nd ed. |
| format | Electronic eBook |
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Any reader who has completed first courses in linear algebra, group theory and ring theory will find this book accessible. The emphasis is on computational techniques but rigorous proofs of all theorems are supplied. This new edition has been revised throughout, including new exercises and an additional chapter on proving that certain groups are infinite.</subfield></datafield><datafield tag="505" ind1="0" ind2=" "><subfield code="a">Cover; Title; Copyright; Dedication; CONTENTS; PREFACE TO THE SECOND EDITION; CHAPTER 1 FREE GROUPS; 1. Definition and elementary properties; 1.1 Definition and elementary properties; 2. Existence of F(X); 1.2 Existence of F(X); 1.3 Further properties of F(X); 3. Further properties of F(X); 1.3 Further properties of F(X); Exercises; CHAPTER 2 SCHREIER'S METHOD; 1. The well-ordering of F; 2.1 The well-ordering of F; 2. The Schreier transversal; 2.2 The Schreier transversal; 3. The Schreier generators; 4. Decomposition of the set A; 5. Freeness of the generators B; 6. Conclusion; Exercises</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">CHAPTER 3 NIELSEN'S METHOD1. The finitely-generated case; 2. Example 1; 3. The general case; 4. Further applications; Exercises; CHAPTER 4 FREE PRESENTATIONS OF GROUPS; 1. Basic concepts; 2. Induced homomorphisms; 3. Direct products; 4. Tietze transformations; 5. van Kampen diagrams; Exercises; CHAPTER 5 SOME POPULAR GROUPS; 1. The quaternions; 2. The Heisenberg group; 3. Symmetric groups; 4. Semi-direct products; 5. Groups of symmetries; 6. Polynomials under substitution; 7. The rational numbers; Exercises; CHAPTER 6 FINITELY-GENERATED ABELIAN GROUPS; 1. Groups-made-abelian</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">2. Free abelian groups3. Change of generators; 4. The invariant factor theorem for matrices; 5. The basis theorem; Exercises; CHAPTER 7 FINITE GROUPS WITH FEW RELATIONS; 1. Metacyclic groups; 2. 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| id | ZDB-4-EBA-ocn817925523 |
| illustrated | Illustrated |
| indexdate | 2024-10-25T16:21:08Z |
| institution | BVB |
| isbn | 9781139168410 113916841X 9781107089037 1107089034 9781107095236 1107095239 |
| language | English |
| oclc_num | 817925523 |
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| physical | 1 online resource (x, 216 pages) : illustrations |
| psigel | ZDB-4-EBA |
| publishDate | 1997 |
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| publisher | Cambridge University Press, |
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| series | London Mathematical Society student texts ; |
| series2 | London Mathematical Society student texts ; |
| spelling | Johnson, D. L. Presentations of groups / D.L. Johnson. 2nd ed. Cambridge, U.K. ; New York, NY, USA : Cambridge University Press, 1997. 1 online resource (x, 216 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier London Mathematical Society student texts ; 15 Includes bibliographical references (pages 201-209) and index. Print version record. The aim of this book is to provide an introduction to combinatorial group theory. Any reader who has completed first courses in linear algebra, group theory and ring theory will find this book accessible. The emphasis is on computational techniques but rigorous proofs of all theorems are supplied. This new edition has been revised throughout, including new exercises and an additional chapter on proving that certain groups are infinite. Cover; Title; Copyright; Dedication; CONTENTS; PREFACE TO THE SECOND EDITION; CHAPTER 1 FREE GROUPS; 1. Definition and elementary properties; 1.1 Definition and elementary properties; 2. Existence of F(X); 1.2 Existence of F(X); 1.3 Further properties of F(X); 3. Further properties of F(X); 1.3 Further properties of F(X); Exercises; CHAPTER 2 SCHREIER'S METHOD; 1. The well-ordering of F; 2.1 The well-ordering of F; 2. The Schreier transversal; 2.2 The Schreier transversal; 3. The Schreier generators; 4. Decomposition of the set A; 5. Freeness of the generators B; 6. Conclusion; Exercises CHAPTER 3 NIELSEN'S METHOD1. The finitely-generated case; 2. Example 1; 3. The general case; 4. Further applications; Exercises; CHAPTER 4 FREE PRESENTATIONS OF GROUPS; 1. Basic concepts; 2. Induced homomorphisms; 3. Direct products; 4. Tietze transformations; 5. van Kampen diagrams; Exercises; CHAPTER 5 SOME POPULAR GROUPS; 1. The quaternions; 2. The Heisenberg group; 3. Symmetric groups; 4. Semi-direct products; 5. Groups of symmetries; 6. Polynomials under substitution; 7. The rational numbers; Exercises; CHAPTER 6 FINITELY-GENERATED ABELIAN GROUPS; 1. Groups-made-abelian 2. Free abelian groups3. Change of generators; 4. The invariant factor theorem for matrices; 5. The basis theorem; Exercises; CHAPTER 7 FINITE GROUPS WITH FEW RELATIONS; 1. Metacyclic groups; 2. Interesting groups with three generators; 3. Cyclically-presented groups; Exercises; CHAPTER 8 COSET ENUMERATION; 1. The basic method; 2. A refinement; Exercises; CHAPTER 9 PRESENTATIONS OF SUBGROUPS; 1. The method; 2. Alternating groups; 3. Braid groups; 4. von Dyck groups; 5. Triangle groups; 6. Free products; 7. HNN-extensions; 8. The Schur multiplicator; Exercises CHAPTER 10 PRESENTATIONS OF GROUP ExTENSIONS1. Basic concepts; 2. The main theorem; 3. Special cases; (S) Semi-direct products; (A) Extensions with abelian kernel; (Z) Central extensions; (D) The direct product; 4. Finite p-groups; Exercises; CHAPTER 11 RELATION MODULES; 1. G-modules; 2. The augmentation ideal; 3. Derivations; 4. Free differential calculus; 5. The fundamental isomorphism; Exercises; CHAPTER 12 AN ALGORITHM FOR N/N'; 1. The Jacobian; 2. The proof; 3. Examples; Exercises; CHAPTER 13 FINITE p-GROUPS; 1. Review of elementary properties; 2. Power-commutator presentations 3. mod p modulesExercises; CHAPTER 14 THE NILPOTENT QUOTIENT ALGORITHM; 1. The algorithm; 2. An example; 3. An improvement; Exercises; CHAPTER 15 THE GOLOD-SHAFAREVICH THEOREM; 1. The proof; 2. An example; 3. Related results; Exercises; CHAPTER 16 PROVING SOME GROUPS INFINITE; 1. Dimension subgroups; 2. The Gaschiitz-Newman formulae; 3. Newman's criterion; 4. Fibonacci update; Exercises; Guide to the literature and references; INDEX; Dramatis Personae Presentations of groups (Mathematics) http://id.loc.gov/authorities/subjects/sh85106447 Présentations de groupes (Mathématiques) MATHEMATICS Group Theory. bisacsh Presentations of groups (Mathematics) fast Gruppentheorie gnd TEORIA DOS GRUPOS. larpcal COHOMOLOGIA DE GRUPOS. larpcal ÁLGEBRA HOMOLÓGICA. larpcal ÁLGEBRA. larpcal has work: Presentations of groups (Text) https://id.oclc.org/worldcat/entity/E39PCGR4RqBxkr3bg8xVQ3K6Dm https://id.oclc.org/worldcat/ontology/hasWork Print version: Johnson, D.L. Presentations of groups. 2nd ed. Cambridge, U.K. ; New York, NY, USA : Cambridge University Press, 1997 0521585422 (DLC) 96036823 (OCoLC)35688069 London Mathematical Society student texts ; 15. FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=570482 Volltext CBO01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=570482 Volltext |
| spellingShingle | Johnson, D. L. Presentations of groups / London Mathematical Society student texts ; Cover; Title; Copyright; Dedication; CONTENTS; PREFACE TO THE SECOND EDITION; CHAPTER 1 FREE GROUPS; 1. Definition and elementary properties; 1.1 Definition and elementary properties; 2. Existence of F(X); 1.2 Existence of F(X); 1.3 Further properties of F(X); 3. Further properties of F(X); 1.3 Further properties of F(X); Exercises; CHAPTER 2 SCHREIER'S METHOD; 1. The well-ordering of F; 2.1 The well-ordering of F; 2. The Schreier transversal; 2.2 The Schreier transversal; 3. The Schreier generators; 4. Decomposition of the set A; 5. Freeness of the generators B; 6. Conclusion; Exercises CHAPTER 3 NIELSEN'S METHOD1. The finitely-generated case; 2. Example 1; 3. The general case; 4. Further applications; Exercises; CHAPTER 4 FREE PRESENTATIONS OF GROUPS; 1. Basic concepts; 2. Induced homomorphisms; 3. Direct products; 4. Tietze transformations; 5. van Kampen diagrams; Exercises; CHAPTER 5 SOME POPULAR GROUPS; 1. The quaternions; 2. The Heisenberg group; 3. Symmetric groups; 4. Semi-direct products; 5. Groups of symmetries; 6. Polynomials under substitution; 7. The rational numbers; Exercises; CHAPTER 6 FINITELY-GENERATED ABELIAN GROUPS; 1. Groups-made-abelian 2. Free abelian groups3. Change of generators; 4. The invariant factor theorem for matrices; 5. The basis theorem; Exercises; CHAPTER 7 FINITE GROUPS WITH FEW RELATIONS; 1. Metacyclic groups; 2. Interesting groups with three generators; 3. Cyclically-presented groups; Exercises; CHAPTER 8 COSET ENUMERATION; 1. The basic method; 2. A refinement; Exercises; CHAPTER 9 PRESENTATIONS OF SUBGROUPS; 1. The method; 2. Alternating groups; 3. Braid groups; 4. von Dyck groups; 5. Triangle groups; 6. Free products; 7. HNN-extensions; 8. The Schur multiplicator; Exercises CHAPTER 10 PRESENTATIONS OF GROUP ExTENSIONS1. Basic concepts; 2. The main theorem; 3. Special cases; (S) Semi-direct products; (A) Extensions with abelian kernel; (Z) Central extensions; (D) The direct product; 4. Finite p-groups; Exercises; CHAPTER 11 RELATION MODULES; 1. G-modules; 2. The augmentation ideal; 3. Derivations; 4. Free differential calculus; 5. The fundamental isomorphism; Exercises; CHAPTER 12 AN ALGORITHM FOR N/N'; 1. The Jacobian; 2. The proof; 3. Examples; Exercises; CHAPTER 13 FINITE p-GROUPS; 1. Review of elementary properties; 2. Power-commutator presentations 3. mod p modulesExercises; CHAPTER 14 THE NILPOTENT QUOTIENT ALGORITHM; 1. The algorithm; 2. An example; 3. An improvement; Exercises; CHAPTER 15 THE GOLOD-SHAFAREVICH THEOREM; 1. The proof; 2. An example; 3. Related results; Exercises; CHAPTER 16 PROVING SOME GROUPS INFINITE; 1. Dimension subgroups; 2. The Gaschiitz-Newman formulae; 3. Newman's criterion; 4. Fibonacci update; Exercises; Guide to the literature and references; INDEX; Dramatis Personae Presentations of groups (Mathematics) http://id.loc.gov/authorities/subjects/sh85106447 Présentations de groupes (Mathématiques) MATHEMATICS Group Theory. bisacsh Presentations of groups (Mathematics) fast Gruppentheorie gnd TEORIA DOS GRUPOS. larpcal COHOMOLOGIA DE GRUPOS. larpcal ÁLGEBRA HOMOLÓGICA. larpcal ÁLGEBRA. larpcal |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85106447 |
| title | Presentations of groups / |
| title_auth | Presentations of groups / |
| title_exact_search | Presentations of groups / |
| title_full | Presentations of groups / D.L. Johnson. |
| title_fullStr | Presentations of groups / D.L. Johnson. |
| title_full_unstemmed | Presentations of groups / D.L. Johnson. |
| title_short | Presentations of groups / |
| title_sort | presentations of groups |
| topic | Presentations of groups (Mathematics) http://id.loc.gov/authorities/subjects/sh85106447 Présentations de groupes (Mathématiques) MATHEMATICS Group Theory. bisacsh Presentations of groups (Mathematics) fast Gruppentheorie gnd TEORIA DOS GRUPOS. larpcal COHOMOLOGIA DE GRUPOS. larpcal ÁLGEBRA HOMOLÓGICA. larpcal ÁLGEBRA. larpcal |
| topic_facet | Presentations of groups (Mathematics) Présentations de groupes (Mathématiques) MATHEMATICS Group Theory. Gruppentheorie TEORIA DOS GRUPOS. COHOMOLOGIA DE GRUPOS. ÁLGEBRA HOMOLÓGICA. ÁLGEBRA. |
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