Groups of prime power order.: Volume 3 /
This is the third volume of a comprehensive and elementary treatment of finite p-group theory. Topics covered in this volume: (a) impact of minimal nonabelian subgroups on the structure of p-groups, (b) classification of groups all of whose nonnormal subgroups have the same order, (c) degrees of irr...
Gespeichert in:
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| Weitere Verfasser: | |
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin :
De Gruyter,
2011.
|
| Schriftenreihe: | De Gruyter expositions in mathematics ;
56. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | This is the third volume of a comprehensive and elementary treatment of finite p-group theory. Topics covered in this volume: (a) impact of minimal nonabelian subgroups on the structure of p-groups, (b) classification of groups all of whose nonnormal subgroups have the same order, (c) degrees of irreducible characters of p-groups associated with finite algebras, (d) groups covered by few proper subgroups, (e) p-groups of element breadth 2 and subgroup breadth 1, (f) exact number of subgroups of given order in a metacyclic p-group, (g) soft subgroups, (h) p-groups with a maximal elementary abel. |
| Beschreibung: | 1 online resource (xxv, 639 pages) |
| Bibliographie: | Includes bibliographical references and indexes. |
| ISBN: | 9783110254488 3110254484 9783110207170 3110207176 1283400375 9781283400374 9786613400376 6613400378 |
| ISSN: | 0938-6572 ; |
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| 245 | 1 | 0 | |a Groups of prime power order. |n Volume 3 / |c Yakov Berkovich, Zvonimir Janko. |
| 260 | |a Berlin : |b De Gruyter, |c 2011. | ||
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| 490 | 0 | |a Groups of prime power order ; |v v. 3 | |
| 504 | |a Includes bibliographical references and indexes. | ||
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| 505 | 0 | |a List of definitions and notations; Preface; Prerequisites from Volumes 1 and 2; 93 Nonabelian 2-groups all of whose minimal nonabelian subgroups are metacyclic and have exponent 4; 94 Nonabelian 2-groups all of whose minimal nonabelian subgroups are nonmetacyclic and have exponent 4; 95 Nonabelian 2-groups of exponent 2e which have no minimal nonabelian subgroups of exponent 2e; 96 Groups with at most two conjugate classes of nonnormal subgroups; 97 p-groups in which some subgroups are generated by elements of order p | |
| 505 | 8 | |a 98 Nonabelian 2-groups all of whose minimal nonabelian subgroups are isomorphic to M2n+1, n? 3 fixed99 2-groups with sectional rank at most 4; 100 2-groups with exactly one maximal subgroup which is neither abelian nor minimal nonabelian; 101 p-groups G with p > 2 and d(G) = 2 having exactly one maximal subgroup which is neither abelian nor minimal nonabelian; 102 p-groups G with p > 2 and d(G) > 2 having exactly one maximal subgroup which is neither abelian nor minimal nonabelian; 103 Some results of Jonah and Konvisser | |
| 505 | 8 | |a 104 Degrees of irreducible characters of p-groups associated with finite algebras105 On some special p-groups; 106 On maximal subgroups of two-generator 2-groups; 107 Ranks of maximal subgroups of nonmetacyclic two-generator 2-groups; 108 p-groups with few conjugate classes of minimal nonabelian subgroups; 109 On p-groups with metacyclic maximal subgroup without cyclic subgroup of index p; 110 Equilibrated p-groups; 111 Characterization of abelian and minimal nonabelian groups; 112 Non-Dedekindian p-groups all of whose nonnormal subgroups have the same order | |
| 505 | 8 | |a 113 The class of 2-groups in 70 is not bounded114 Further counting theorems; 115 Finite p-groups all of whose maximal subgroups except one are extraspecial; 116 Groups covered by few proper subgroups; 117 2-groups all of whose nonnormal subgroups are either cyclic or of maximal class; 118 Review of characterizations of p-groups with various minimal nonabelian subgroups; 119 Review of characterizations of p-groups of maximal class; 120 Nonabelian 2-groups such that any two distinct minimal nonabelian subgroups have cyclic intersection; 121 p-groups of breadth 2 | |
| 505 | 8 | |a 122 p-groups all of whose subgroups have normalizers of index at most p123 Subgroups of finite groups generated by all elements in two shortest conjugacy classes; 124 The number of subgroups of given order in a metacyclic p-group; 125 p-groups G containing a maximal subgroup H all of whose subgroups are G-invariant; 126 The existence of p-groups G1 < G such that Aut(G1) ? Aut(G); 127 On 2-groups containing a maximal elementary abelian subgroup of order 4; 128 The commutator subgroup of p-groups with the subgroup breadth 1 | |
| 520 | |a This is the third volume of a comprehensive and elementary treatment of finite p-group theory. Topics covered in this volume: (a) impact of minimal nonabelian subgroups on the structure of p-groups, (b) classification of groups all of whose nonnormal subgroups have the same order, (c) degrees of irreducible characters of p-groups associated with finite algebras, (d) groups covered by few proper subgroups, (e) p-groups of element breadth 2 and subgroup breadth 1, (f) exact number of subgroups of given order in a metacyclic p-group, (g) soft subgroups, (h) p-groups with a maximal elementary abel. | ||
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| author | Berkovich, I︠A︡. G., 1938- |
| author2 | Janko, Zvonimir, 1932- |
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| contents | List of definitions and notations; Preface; Prerequisites from Volumes 1 and 2; 93 Nonabelian 2-groups all of whose minimal nonabelian subgroups are metacyclic and have exponent 4; 94 Nonabelian 2-groups all of whose minimal nonabelian subgroups are nonmetacyclic and have exponent 4; 95 Nonabelian 2-groups of exponent 2e which have no minimal nonabelian subgroups of exponent 2e; 96 Groups with at most two conjugate classes of nonnormal subgroups; 97 p-groups in which some subgroups are generated by elements of order p 98 Nonabelian 2-groups all of whose minimal nonabelian subgroups are isomorphic to M2n+1, n? 3 fixed99 2-groups with sectional rank at most 4; 100 2-groups with exactly one maximal subgroup which is neither abelian nor minimal nonabelian; 101 p-groups G with p > 2 and d(G) = 2 having exactly one maximal subgroup which is neither abelian nor minimal nonabelian; 102 p-groups G with p > 2 and d(G) > 2 having exactly one maximal subgroup which is neither abelian nor minimal nonabelian; 103 Some results of Jonah and Konvisser 104 Degrees of irreducible characters of p-groups associated with finite algebras105 On some special p-groups; 106 On maximal subgroups of two-generator 2-groups; 107 Ranks of maximal subgroups of nonmetacyclic two-generator 2-groups; 108 p-groups with few conjugate classes of minimal nonabelian subgroups; 109 On p-groups with metacyclic maximal subgroup without cyclic subgroup of index p; 110 Equilibrated p-groups; 111 Characterization of abelian and minimal nonabelian groups; 112 Non-Dedekindian p-groups all of whose nonnormal subgroups have the same order 113 The class of 2-groups in 70 is not bounded114 Further counting theorems; 115 Finite p-groups all of whose maximal subgroups except one are extraspecial; 116 Groups covered by few proper subgroups; 117 2-groups all of whose nonnormal subgroups are either cyclic or of maximal class; 118 Review of characterizations of p-groups with various minimal nonabelian subgroups; 119 Review of characterizations of p-groups of maximal class; 120 Nonabelian 2-groups such that any two distinct minimal nonabelian subgroups have cyclic intersection; 121 p-groups of breadth 2 122 p-groups all of whose subgroups have normalizers of index at most p123 Subgroups of finite groups generated by all elements in two shortest conjugacy classes; 124 The number of subgroups of given order in a metacyclic p-group; 125 p-groups G containing a maximal subgroup H all of whose subgroups are G-invariant; 126 The existence of p-groups G1 < G such that Aut(G1) ? Aut(G); 127 On 2-groups containing a maximal elementary abelian subgroup of order 4; 128 The commutator subgroup of p-groups with the subgroup breadth 1 |
| ctrlnum | (OCoLC)747413860 |
| dewey-full | 512/.23 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.23 |
| dewey-search | 512/.23 |
| dewey-sort | 3512 223 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| oclc_num | 747413860 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (xxv, 639 pages) |
| psigel | ZDB-4-EBA |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | De Gruyter, |
| record_format | marc |
| series | De Gruyter expositions in mathematics ; |
| series2 | De Gruyter expositions in mathematics, Groups of prime power order ; |
| 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 3 / Yakov Berkovich, Zvonimir Janko. Berlin : De Gruyter, 2011. 1 online resource (xxv, 639 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier De Gruyter expositions in mathematics, 0938-6572 ; 56 Groups of prime power order ; v. 3 Includes bibliographical references and indexes. Print version record. List of definitions and notations; Preface; Prerequisites from Volumes 1 and 2; 93 Nonabelian 2-groups all of whose minimal nonabelian subgroups are metacyclic and have exponent 4; 94 Nonabelian 2-groups all of whose minimal nonabelian subgroups are nonmetacyclic and have exponent 4; 95 Nonabelian 2-groups of exponent 2e which have no minimal nonabelian subgroups of exponent 2e; 96 Groups with at most two conjugate classes of nonnormal subgroups; 97 p-groups in which some subgroups are generated by elements of order p 98 Nonabelian 2-groups all of whose minimal nonabelian subgroups are isomorphic to M2n+1, n? 3 fixed99 2-groups with sectional rank at most 4; 100 2-groups with exactly one maximal subgroup which is neither abelian nor minimal nonabelian; 101 p-groups G with p > 2 and d(G) = 2 having exactly one maximal subgroup which is neither abelian nor minimal nonabelian; 102 p-groups G with p > 2 and d(G) > 2 having exactly one maximal subgroup which is neither abelian nor minimal nonabelian; 103 Some results of Jonah and Konvisser 104 Degrees of irreducible characters of p-groups associated with finite algebras105 On some special p-groups; 106 On maximal subgroups of two-generator 2-groups; 107 Ranks of maximal subgroups of nonmetacyclic two-generator 2-groups; 108 p-groups with few conjugate classes of minimal nonabelian subgroups; 109 On p-groups with metacyclic maximal subgroup without cyclic subgroup of index p; 110 Equilibrated p-groups; 111 Characterization of abelian and minimal nonabelian groups; 112 Non-Dedekindian p-groups all of whose nonnormal subgroups have the same order 113 The class of 2-groups in 70 is not bounded114 Further counting theorems; 115 Finite p-groups all of whose maximal subgroups except one are extraspecial; 116 Groups covered by few proper subgroups; 117 2-groups all of whose nonnormal subgroups are either cyclic or of maximal class; 118 Review of characterizations of p-groups with various minimal nonabelian subgroups; 119 Review of characterizations of p-groups of maximal class; 120 Nonabelian 2-groups such that any two distinct minimal nonabelian subgroups have cyclic intersection; 121 p-groups of breadth 2 122 p-groups all of whose subgroups have normalizers of index at most p123 Subgroups of finite groups generated by all elements in two shortest conjugacy classes; 124 The number of subgroups of given order in a metacyclic p-group; 125 p-groups G containing a maximal subgroup H all of whose subgroups are G-invariant; 126 The existence of p-groups G1 < G such that Aut(G1) ? Aut(G); 127 On 2-groups containing a maximal elementary abelian subgroup of order 4; 128 The commutator subgroup of p-groups with the subgroup breadth 1 This is the third volume of a comprehensive and elementary treatment of finite p-group theory. Topics covered in this volume: (a) impact of minimal nonabelian subgroups on the structure of p-groups, (b) classification of groups all of whose nonnormal subgroups have the same order, (c) degrees of irreducible characters of p-groups associated with finite algebras, (d) groups covered by few proper subgroups, (e) p-groups of element breadth 2 and subgroup breadth 1, (f) exact number of subgroups of given order in a metacyclic p-group, (g) soft subgroups, (h) p-groups with a maximal elementary abel. English. 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 Janko, Zvonimir, 1932- https://id.oclc.org/worldcat/entity/E39PBJrGwd49wjWFDwdVGKH3cP http://id.loc.gov/authorities/names/n2011014887 Print version: 9783110207170 De Gruyter expositions in mathematics ; 56. 0938-6572 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=381766 Volltext |
| spellingShingle | Berkovich, I︠A︡. G., 1938- Groups of prime power order. De Gruyter expositions in mathematics ; List of definitions and notations; Preface; Prerequisites from Volumes 1 and 2; 93 Nonabelian 2-groups all of whose minimal nonabelian subgroups are metacyclic and have exponent 4; 94 Nonabelian 2-groups all of whose minimal nonabelian subgroups are nonmetacyclic and have exponent 4; 95 Nonabelian 2-groups of exponent 2e which have no minimal nonabelian subgroups of exponent 2e; 96 Groups with at most two conjugate classes of nonnormal subgroups; 97 p-groups in which some subgroups are generated by elements of order p 98 Nonabelian 2-groups all of whose minimal nonabelian subgroups are isomorphic to M2n+1, n? 3 fixed99 2-groups with sectional rank at most 4; 100 2-groups with exactly one maximal subgroup which is neither abelian nor minimal nonabelian; 101 p-groups G with p > 2 and d(G) = 2 having exactly one maximal subgroup which is neither abelian nor minimal nonabelian; 102 p-groups G with p > 2 and d(G) > 2 having exactly one maximal subgroup which is neither abelian nor minimal nonabelian; 103 Some results of Jonah and Konvisser 104 Degrees of irreducible characters of p-groups associated with finite algebras105 On some special p-groups; 106 On maximal subgroups of two-generator 2-groups; 107 Ranks of maximal subgroups of nonmetacyclic two-generator 2-groups; 108 p-groups with few conjugate classes of minimal nonabelian subgroups; 109 On p-groups with metacyclic maximal subgroup without cyclic subgroup of index p; 110 Equilibrated p-groups; 111 Characterization of abelian and minimal nonabelian groups; 112 Non-Dedekindian p-groups all of whose nonnormal subgroups have the same order 113 The class of 2-groups in 70 is not bounded114 Further counting theorems; 115 Finite p-groups all of whose maximal subgroups except one are extraspecial; 116 Groups covered by few proper subgroups; 117 2-groups all of whose nonnormal subgroups are either cyclic or of maximal class; 118 Review of characterizations of p-groups with various minimal nonabelian subgroups; 119 Review of characterizations of p-groups of maximal class; 120 Nonabelian 2-groups such that any two distinct minimal nonabelian subgroups have cyclic intersection; 121 p-groups of breadth 2 122 p-groups all of whose subgroups have normalizers of index at most p123 Subgroups of finite groups generated by all elements in two shortest conjugacy classes; 124 The number of subgroups of given order in a metacyclic p-group; 125 p-groups G containing a maximal subgroup H all of whose subgroups are G-invariant; 126 The existence of p-groups G1 < G such that Aut(G1) ? Aut(G); 127 On 2-groups containing a maximal elementary abelian subgroup of order 4; 128 The commutator subgroup of p-groups with the subgroup breadth 1 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 3 / Yakov Berkovich, Zvonimir Janko. |
| title_fullStr | Groups of prime power order. Volume 3 / Yakov Berkovich, Zvonimir Janko. |
| title_full_unstemmed | Groups of prime power order. Volume 3 / Yakov Berkovich, Zvonimir Janko. |
| 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=381766 |
| work_keys_str_mv | AT berkovichiag groupsofprimepowerordervolume3 AT jankozvonimir groupsofprimepowerordervolume3 |