Complementation of Normal Subgroups: In Finite Groups

Joseph Kirtland

Published by De Gruyter 2017

Complementation of Normal Subgroups

In Finite Groups

Joseph Kirtland

https://doi.org/10.1515/9783110480214

Overview
Contents

About this book

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.

Contents
Prerequisites
The Schur-Zassenhaus theorem: A bit of history and motivation
Abelian and minimal normal subgroups
Reduction theorems
Subgroups in the chief series, derived series, and lower nilpotent series
Normal subgroups with abelian sylow subgroups
The formation generation
Groups with specific classes of subgroups complemented

Author / Editor information

Joseph Kirtland, Marist College, NY, USA.

Reviews

"This book includes many interesting historical remarks and discusses the topic of complementation from many different perspectives, which makes it a valuable reference point on the subject."
Rebecca A. H. Waldecker in: Mathematical Reviews Clippings (10.2018), MR3727140

Topics

Frontmatter Publicly Available Download PDF	i
Preface Requires Authentication Unlicensed Licensed Download PDF	vii
Contents Publicly Available Download PDF	ix
Notation Requires Authentication Unlicensed Licensed Download PDF	xi
1. Prerequisites Requires Authentication Unlicensed Licensed Download PDF	1
2. The Schur-Zassenhaus theorem: A bit of history and motivation Requires Authentication Unlicensed Licensed Download PDF	43
3. Abelian and minimal normal subgroups Requires Authentication Unlicensed Licensed Download PDF	57
4. Reduction theorems Requires Authentication Unlicensed Licensed Download PDF	69
5. Subgroups in the chief series, derived series, and lower nilpotent series Requires Authentication Unlicensed Licensed Download PDF	79
6. Normal subgroups with abelian sylow subgroups Requires Authentication Unlicensed Licensed Download PDF	91
7. The formation generation Requires Authentication Unlicensed Licensed Download PDF	97
8. Groups with specific classes of subgroups complemented Requires Authentication Unlicensed Licensed Download PDF	109
Bibliography Requires Authentication Unlicensed Licensed Download PDF	137
Author index Requires Authentication Unlicensed Licensed Download PDF	141
Subject index Requires Authentication Unlicensed Licensed Download PDF	143

(Deutsch)

Language: English
Publisher: De Gruyter
Audience: Researchers in Mathematics.
Pages
- Front matter: 12
- Main content: 144
Keywords: Normale Gruppe; Untergruppe

eBook

Published: September 11, 2017
ISBN: 9783110480214

Hardcover

Published: September 11, 2017
ISBN: 9783110478792