Groups of prime power order.: Volume 1 /
This is the first of three volumes on finite p-group theory. It presents the state of the art and in addition contains numerous new and easy proofs of famous theorems, many exercises (some of them with solutions), and about 1500 open problems. It is expected to be useful to certain applied mathemati...
Gespeichert in:
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin ; New York :
W. de Gruyter,
©2008.
|
| Schriftenreihe: | De Gruyter expositions in mathematics ;
46. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | This is the first of three volumes on finite p-group theory. It presents the state of the art and in addition contains numerous new and easy proofs of famous theorems, many exercises (some of them with solutions), and about 1500 open problems. It is expected to be useful to certain applied mathematics areas, such as combinatorics, coding theory, and computer sciences. The book should also be easily comprehensible to students and scientists with some basic knowledge of group theory and algebra. |
| Beschreibung: | "This is the first of three volumes of a comprehensive and elementary treatment of finite p-group theory"--Page 4 of cover, v. 1 |
| Beschreibung: | 1 online resource (xx, 512 pages) |
| Bibliographie: | Includes bibliographical references (pages 480-504) and indexes. |
| ISBN: | 9783110208221 3110208229 |
| ISSN: | 0938-6572 ; |
Internformat
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| 245 | 1 | 0 | |a Groups of prime power order. |n Volume 1 / |c by Yakov Berkovich. |
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| 500 | |a "This is the first of three volumes of a comprehensive and elementary treatment of finite p-group theory"--Page 4 of cover, v. 1 | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a Frontmatter; Contents; List of definitions and notations; Foreword; Preface; Introduction; 1. Groups with a cyclic subgroup of index p. Frattini subgroup. Varia; 2. The class number, character degrees; 3. Minimal classes; 4. p-groups with cyclic Frattini subgroup; 5. Hall's enumeration principle; 6. q'-automorphisms of q-groups; 7. Regular p-groups; 8. Pyramidal p-groups; 9. On p-groups of maximal class; 10. On abelian subgroups of p-groups; 11. On the power structure of a p-group; 12. Counting theorems for p-groups of maximal class; 13. Further counting theorems. | |
| 505 | 8 | |a 14. Thompson's critical subgroup; 15. Generators of p-groups; 16. Classification of finite p-groups all of whose noncyclic subgroups are normal; 17. Counting theorems for regular p-groups; 18. Counting theorems for irregular p-groups; 19. Some additional counting theorems; 20. Groups with small abelian subgroups and partitions; 21. On the Schur multiplier and the commutator subgroup; 22. On characters of p-groups; 23. On subgroups of given exponent; 24. Hall's theorem on normal subgroups of given exponent; 25. On the lattice of subgroups of a group; 26. Powerful p-groups. | |
| 505 | 8 | |a 27. p-groups with normal centralizers of all elements; 28. p-groups with a uniqueness condition for nonnormal subgroups; 29. On isoclinism; 30. On p-groups with few nonabelian subgroups of order pp and exponent p; 31. On p-groups with small p0-groups of operators; 32. W. Gaschütz's and P. Schmid's theorems on p-automorphisms of p-groups; 33. Groups of order pm with automorphisms of order pm-1, pm-2 or pm-3; 34. Nilpotent groups of automorphisms; 35. Maximal abelian subgroups of p-groups; 36. Short proofs of some basic characterization theorems of finite p-group theory. | |
| 505 | 8 | |a 37. MacWilliams' theorem; 38. p-groups with exactly two conjugate classes of subgroups of small orders and exponent p>2; 39. Alperin's problem on abelian subgroups of small index; 40. On breadth and class number of p-groups; 41. Groups in which every two noncyclic subgroups of the same order have the same rank; 42. On intersections of some subgroups; 43. On 2-groups with few cyclic subgroups of given order; 44. Some characterizations of metacyclic p-groups; 45. A counting theorem for p-groups of odd order; Appendix 1. The Hall-Petrescu formula. | |
| 505 | 8 | |a Appendix 2. Mann's proof of monomiality of p-groups; Appendix 3. Theorems of Isaacs on actions of groups; Appendix 4. Freiman's number-theoretical theorems; Appendix 5. Another proof of Theorem 5.4; Appendix 6. On the order of p-groups of given derived length; Appendix 7. Relative indices of elements of p-groups; Appendix 8. p-groups withabsolutely regular Frattini subgroup; Appendix 9. On characteristic subgroups of metacyclic groups; Appendix 10. On minimal characters of p-groups; Appendix 11. On sums of degrees of irreducible characters. | |
| 520 | |a This is the first of three volumes on finite p-group theory. It presents the state of the art and in addition contains numerous new and easy proofs of famous theorems, many exercises (some of them with solutions), and about 1500 open problems. It is expected to be useful to certain applied mathematics areas, such as combinatorics, coding theory, and computer sciences. The book should also be easily comprehensible to students and scientists with some basic knowledge of group theory and algebra. | ||
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| 650 | 0 | |a Group theory. |0 http://id.loc.gov/authorities/subjects/sh85057512 | |
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| author | Berkovich, I︠A︡. G., 1938- |
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| contents | Frontmatter; Contents; List of definitions and notations; Foreword; Preface; Introduction; 1. Groups with a cyclic subgroup of index p. Frattini subgroup. Varia; 2. The class number, character degrees; 3. Minimal classes; 4. p-groups with cyclic Frattini subgroup; 5. Hall's enumeration principle; 6. q'-automorphisms of q-groups; 7. Regular p-groups; 8. Pyramidal p-groups; 9. On p-groups of maximal class; 10. On abelian subgroups of p-groups; 11. On the power structure of a p-group; 12. Counting theorems for p-groups of maximal class; 13. Further counting theorems. 14. Thompson's critical subgroup; 15. Generators of p-groups; 16. Classification of finite p-groups all of whose noncyclic subgroups are normal; 17. Counting theorems for regular p-groups; 18. Counting theorems for irregular p-groups; 19. Some additional counting theorems; 20. Groups with small abelian subgroups and partitions; 21. On the Schur multiplier and the commutator subgroup; 22. On characters of p-groups; 23. On subgroups of given exponent; 24. Hall's theorem on normal subgroups of given exponent; 25. On the lattice of subgroups of a group; 26. Powerful p-groups. 27. p-groups with normal centralizers of all elements; 28. p-groups with a uniqueness condition for nonnormal subgroups; 29. On isoclinism; 30. On p-groups with few nonabelian subgroups of order pp and exponent p; 31. On p-groups with small p0-groups of operators; 32. W. Gaschütz's and P. Schmid's theorems on p-automorphisms of p-groups; 33. Groups of order pm with automorphisms of order pm-1, pm-2 or pm-3; 34. Nilpotent groups of automorphisms; 35. Maximal abelian subgroups of p-groups; 36. Short proofs of some basic characterization theorems of finite p-group theory. 37. MacWilliams' theorem; 38. p-groups with exactly two conjugate classes of subgroups of small orders and exponent p>2; 39. Alperin's problem on abelian subgroups of small index; 40. On breadth and class number of p-groups; 41. Groups in which every two noncyclic subgroups of the same order have the same rank; 42. On intersections of some subgroups; 43. On 2-groups with few cyclic subgroups of given order; 44. Some characterizations of metacyclic p-groups; 45. A counting theorem for p-groups of odd order; Appendix 1. The Hall-Petrescu formula. Appendix 2. Mann's proof of monomiality of p-groups; Appendix 3. Theorems of Isaacs on actions of groups; Appendix 4. Freiman's number-theoretical theorems; Appendix 5. Another proof of Theorem 5.4; Appendix 6. On the order of p-groups of given derived length; Appendix 7. Relative indices of elements of p-groups; Appendix 8. p-groups withabsolutely regular Frattini subgroup; Appendix 9. On characteristic subgroups of metacyclic groups; Appendix 10. On minimal characters of p-groups; Appendix 11. On sums of degrees of irreducible characters. |
| ctrlnum | (OCoLC)402487701 |
| dewey-full | 512.2 |
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| dewey-ones | 512 - Algebra |
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| discipline | Mathematik |
| format | Electronic eBook |
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| series | De Gruyter expositions in mathematics ; |
| series2 | De Gruyter expositions in mathematics, |
| spelling | Berkovich, I︠A︡. G., 1938- https://id.oclc.org/worldcat/entity/E39PCjCrW6hTDygx3j7wTWPgmm http://id.loc.gov/authorities/names/n97085489 Groups of prime power order. Volume 1 / by Yakov Berkovich. Berlin ; New York : W. de Gruyter, ©2008. 1 online resource (xx, 512 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier De Gruyter expositions in mathematics, 0938-6572 ; 46 Includes bibliographical references (pages 480-504) and indexes. "This is the first of three volumes of a comprehensive and elementary treatment of finite p-group theory"--Page 4 of cover, v. 1 Print version record. Frontmatter; Contents; List of definitions and notations; Foreword; Preface; Introduction; 1. Groups with a cyclic subgroup of index p. Frattini subgroup. Varia; 2. The class number, character degrees; 3. Minimal classes; 4. p-groups with cyclic Frattini subgroup; 5. Hall's enumeration principle; 6. q'-automorphisms of q-groups; 7. Regular p-groups; 8. Pyramidal p-groups; 9. On p-groups of maximal class; 10. On abelian subgroups of p-groups; 11. On the power structure of a p-group; 12. Counting theorems for p-groups of maximal class; 13. Further counting theorems. 14. Thompson's critical subgroup; 15. Generators of p-groups; 16. Classification of finite p-groups all of whose noncyclic subgroups are normal; 17. Counting theorems for regular p-groups; 18. Counting theorems for irregular p-groups; 19. Some additional counting theorems; 20. Groups with small abelian subgroups and partitions; 21. On the Schur multiplier and the commutator subgroup; 22. On characters of p-groups; 23. On subgroups of given exponent; 24. Hall's theorem on normal subgroups of given exponent; 25. On the lattice of subgroups of a group; 26. Powerful p-groups. 27. p-groups with normal centralizers of all elements; 28. p-groups with a uniqueness condition for nonnormal subgroups; 29. On isoclinism; 30. On p-groups with few nonabelian subgroups of order pp and exponent p; 31. On p-groups with small p0-groups of operators; 32. W. Gaschütz's and P. Schmid's theorems on p-automorphisms of p-groups; 33. Groups of order pm with automorphisms of order pm-1, pm-2 or pm-3; 34. Nilpotent groups of automorphisms; 35. Maximal abelian subgroups of p-groups; 36. Short proofs of some basic characterization theorems of finite p-group theory. 37. MacWilliams' theorem; 38. p-groups with exactly two conjugate classes of subgroups of small orders and exponent p>2; 39. Alperin's problem on abelian subgroups of small index; 40. On breadth and class number of p-groups; 41. Groups in which every two noncyclic subgroups of the same order have the same rank; 42. On intersections of some subgroups; 43. On 2-groups with few cyclic subgroups of given order; 44. Some characterizations of metacyclic p-groups; 45. A counting theorem for p-groups of odd order; Appendix 1. The Hall-Petrescu formula. Appendix 2. Mann's proof of monomiality of p-groups; Appendix 3. Theorems of Isaacs on actions of groups; Appendix 4. Freiman's number-theoretical theorems; Appendix 5. Another proof of Theorem 5.4; Appendix 6. On the order of p-groups of given derived length; Appendix 7. Relative indices of elements of p-groups; Appendix 8. p-groups withabsolutely regular Frattini subgroup; Appendix 9. On characteristic subgroups of metacyclic groups; Appendix 10. On minimal characters of p-groups; Appendix 11. On sums of degrees of irreducible characters. This is the first of three volumes on finite p-group theory. It presents the state of the art and in addition contains numerous new and easy proofs of famous theorems, many exercises (some of them with solutions), and about 1500 open problems. It is expected to be useful to certain applied mathematics areas, such as combinatorics, coding theory, and computer sciences. The book should also be easily comprehensible to students and scientists with some basic knowledge of group theory and algebra. Finite groups. http://id.loc.gov/authorities/subjects/sh85048354 Group theory. http://id.loc.gov/authorities/subjects/sh85057512 Groupes finis. Théorie des groupes. MATHEMATICS Group Theory. bisacsh Finite groups fast Group theory fast has work: Volume 1 Groups of prime power order (Text) https://id.oclc.org/worldcat/entity/E39PCGDfRRqKjCHb8mbMHY4C73 https://id.oclc.org/worldcat/ontology/hasWork Print version: Berkovich, I︠A︡. G., 1938- Groups of prime power order. Volume 1. Berlin ; New York : W. de Gruyter, ©2008 9783110204186 De Gruyter expositions in mathematics ; 46. http://id.loc.gov/authorities/names/n90653843 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=274367 Volltext |
| spellingShingle | Berkovich, I︠A︡. G., 1938- Groups of prime power order. De Gruyter expositions in mathematics ; Frontmatter; Contents; List of definitions and notations; Foreword; Preface; Introduction; 1. Groups with a cyclic subgroup of index p. Frattini subgroup. Varia; 2. The class number, character degrees; 3. Minimal classes; 4. p-groups with cyclic Frattini subgroup; 5. Hall's enumeration principle; 6. q'-automorphisms of q-groups; 7. Regular p-groups; 8. Pyramidal p-groups; 9. On p-groups of maximal class; 10. On abelian subgroups of p-groups; 11. On the power structure of a p-group; 12. Counting theorems for p-groups of maximal class; 13. Further counting theorems. 14. Thompson's critical subgroup; 15. Generators of p-groups; 16. Classification of finite p-groups all of whose noncyclic subgroups are normal; 17. Counting theorems for regular p-groups; 18. Counting theorems for irregular p-groups; 19. Some additional counting theorems; 20. Groups with small abelian subgroups and partitions; 21. On the Schur multiplier and the commutator subgroup; 22. On characters of p-groups; 23. On subgroups of given exponent; 24. Hall's theorem on normal subgroups of given exponent; 25. On the lattice of subgroups of a group; 26. Powerful p-groups. 27. p-groups with normal centralizers of all elements; 28. p-groups with a uniqueness condition for nonnormal subgroups; 29. On isoclinism; 30. On p-groups with few nonabelian subgroups of order pp and exponent p; 31. On p-groups with small p0-groups of operators; 32. W. Gaschütz's and P. Schmid's theorems on p-automorphisms of p-groups; 33. Groups of order pm with automorphisms of order pm-1, pm-2 or pm-3; 34. Nilpotent groups of automorphisms; 35. Maximal abelian subgroups of p-groups; 36. Short proofs of some basic characterization theorems of finite p-group theory. 37. MacWilliams' theorem; 38. p-groups with exactly two conjugate classes of subgroups of small orders and exponent p>2; 39. Alperin's problem on abelian subgroups of small index; 40. On breadth and class number of p-groups; 41. Groups in which every two noncyclic subgroups of the same order have the same rank; 42. On intersections of some subgroups; 43. On 2-groups with few cyclic subgroups of given order; 44. Some characterizations of metacyclic p-groups; 45. A counting theorem for p-groups of odd order; Appendix 1. The Hall-Petrescu formula. Appendix 2. Mann's proof of monomiality of p-groups; Appendix 3. Theorems of Isaacs on actions of groups; Appendix 4. Freiman's number-theoretical theorems; Appendix 5. Another proof of Theorem 5.4; Appendix 6. On the order of p-groups of given derived length; Appendix 7. Relative indices of elements of p-groups; Appendix 8. p-groups withabsolutely regular Frattini subgroup; Appendix 9. On characteristic subgroups of metacyclic groups; Appendix 10. On minimal characters of p-groups; Appendix 11. On sums of degrees of irreducible characters. Finite groups. http://id.loc.gov/authorities/subjects/sh85048354 Group theory. http://id.loc.gov/authorities/subjects/sh85057512 Groupes finis. Théorie des groupes. MATHEMATICS Group Theory. bisacsh Finite groups fast Group theory fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85048354 http://id.loc.gov/authorities/subjects/sh85057512 |
| title | Groups of prime power order. |
| title_auth | Groups of prime power order. |
| title_exact_search | Groups of prime power order. |
| title_full | Groups of prime power order. Volume 1 / by Yakov Berkovich. |
| title_fullStr | Groups of prime power order. Volume 1 / by Yakov Berkovich. |
| title_full_unstemmed | Groups of prime power order. Volume 1 / by Yakov Berkovich. |
| title_short | Groups of prime power order. |
| title_sort | groups of prime power order |
| topic | Finite groups. http://id.loc.gov/authorities/subjects/sh85048354 Group theory. http://id.loc.gov/authorities/subjects/sh85057512 Groupes finis. Théorie des groupes. MATHEMATICS Group Theory. bisacsh Finite groups fast Group theory fast |
| topic_facet | Finite groups. Group theory. Groupes finis. Théorie des groupes. MATHEMATICS Group Theory. Finite groups Group theory |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=274367 |
| work_keys_str_mv | AT berkovichiag groupsofprimepowerordervolume1 |