Complementation of normal subgroups : in finite groups

Starting with the Schur-Zassenhaus theorem, this monograph documents a wide variety of results concerning complementation of normal subgroups in finite groups. The contents cover a wide range of material from reduction theorems and subgroups in the derived and lower nilpotent series to abelian norma...

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Main Author Kirtland, Joseph
Format eBook Book
LanguageEnglish
Published Berlin De Gruyter 2017
Walter de Gruyter GmbH
Edition1
Subjects
Finite groups
MATHEMATICS / Group Theory
Normale Gruppe
Sylow subgroups
Untergruppe
Online AccessGet full text
ISBN9783110478792
311047879X
DOI10.1515/9783110480214

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Abstract Starting with the Schur-Zassenhaus theorem, this monograph documents a wide variety of results concerning complementation of normal subgroups in finite groups. The contents cover a wide range of material from reduction theorems and subgroups in the derived and lower nilpotent series to abelian normal subgroups and formations. ContentsPrerequisitesThe Schur-Zassenhaus theorem: A bit of history and motivationAbelian and minimal normal subgroupsReduction theoremsSubgroups in the chief series, derived series, and lower nilpotent seriesNormal subgroups with abelian sylow subgroupsThe formation generationGroups with specific classes of subgroups complemented
AbstractList Starting with the Schur-Zassenhaus theorem, this monograph documents a wide variety of results concerning complementation of normal subgroups in finite groups. The contents cover a wide range of material from reduction theorems and subgroups in the derived and lower nilpotent series to abelian normal subgroups and formations. ContentsPrerequisitesThe Schur-Zassenhaus theorem: A bit of history and motivationAbelian and minimal normal subgroupsReduction theoremsSubgroups in the chief series, derived series, and lower nilpotent seriesNormal subgroups with abelian sylow subgroupsThe formation generationGroups with specific classes of subgroups complemented
Starting with the Schur-Zassenhaus theorem, this monograph documents a wide variety of results concerning complementation of normal subgroups in finite groups. The contents cover a wide range of material from reduction theorems and subgroups in the derived and lower nilpotent series to abelian normal subgroups and formations.
Author Kirtland, Joseph
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Notes Includes bibliographical references (p. [137]-140) and indexes
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Snippet Starting with the Schur-Zassenhaus theorem, this monograph documents a wide variety of results concerning complementation of normal subgroups in finite groups....
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SubjectTerms Finite groups
MATHEMATICS / Group Theory
Normale Gruppe
Sylow subgroups
Untergruppe
TableOfContents Intro -- Preface -- Contents -- Notation -- 1. Prerequisites -- 2. The Schur-Zassenhaus theorem: A bit of history and motivation -- 3. Abelian and minimal normal subgroups -- 4. Reduction theorems -- 5. Subgroups in the chief series, derived series, and lower nilpotent series -- 6. Normal subgroups with abelian sylow subgroups -- 7. The formation generation -- 8. Groups with specific classes of subgroups complemented -- Bibliography -- Author index -- Subject index
Subject index
Contents --
6. Normal subgroups with abelian sylow subgroups --
Preface --
1. Prerequisites --
4. Reduction theorems --
3. Abelian and minimal normal subgroups --
5. Subgroups in the chief series, derived series, and lower nilpotent series --
Notation --
Frontmatter --
7. The formation generation --
Bibliography --
2. The Schur-Zassenhaus theorem: A bit of history and motivation --
8. Groups with specific classes of subgroups complemented --
Author index --
Title Complementation of normal subgroups : in finite groups
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