On unit groups of modular group algebras | The concept of end-commutable ordering - with 241 exercises

Sven Bodo Wirsing

ISBN 10: 3960672241 / ISBN 13: 9783960672241

Published by Anchor Academic Publishing, 2019

About this Item

On unit groups of modular group algebras | The concept of end-commutable ordering - with 241 exercises | Sven Bodo Wirsing | Taschenbuch | 204 S. | Englisch | 2019 | Anchor Academic Publishing | EAN 9783960672241 | Verantwortliche Person für die EU: Dryas Verlag, ein Imprint der Bedey und Thoms Media GmbH, Hermannstal 119k, 22119 Hamburg, kontakt[at]dryas[dot]de | Anbieter: preigu.

Seller Inventory # 117897518

Bibliographic Details

• Title: On unit groups of modular group algebras | The concept of end-commutable ordering - with 241 exercises
• Publisher: Anchor Academic Publishing
• Publication Date: 2019
• Language: English
• ISBN 10: 3960672241
• ISBN 13: 9783960672241
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 220W x 155H x 13D millimeters 220 millimeters width by 155 millimeters height by 13 millimeters depth
• Weight: 333 grams
• Seller catalogs:
  • Bücher

About this title

Synopsis

In this book we analyse unit groups of group algebras KG for non-abelian p-groups G and fields K of characteristic p. By calculating the core and the normaliser of U in 1 + rad(KG) - the group of normalized units -- for every subgroup U of G, we generalise results of K.R. Pearson and D.B. Coleman using fixed points of enhanced group actions. Our concept of so-called end-commutable ordering leads to a new method of studying the center of 1 + rad(KG). We proof that a finite group G is nilpotent if and only if every conjugacy class possesses an end-commutable ordering. As a simple consequence we get a result of A.A. Bovdi and Z. Patay, which shows how the exponent of the center of 1 + rad(KG) can be determined by calculations purely within the group G. We describe the groups for which this exponent is extremal and calculate the exponent for various group classes (e.g. regular groups, special groups, Sylow subgroups of linear and symmetric groups) and group constructions (e.g. wreath products, central products, special group extensions, isoclinic groups). Another application of our concept of end-commutable ordering is a description of the invariants of the center of 1 + rad(KG) for a finite field K. They are determined purely by the group G and the field K and can be visualized by a special graph - the class-graph. As a consequence of our results we prove that the center, the derived subgroups and the p-th-power subgroup of 1 + rad(KG) are not cyclic. Furthermore, we obtain some properties of unit groups of group algebras for extra-special 2-groups and fields of characteristic 2. Finally, we investigate the behaviour of the center and other characteristics (e.g. the exponent, the class of nilpotency, the Baer length, the degree of commutativity) for the chain of iterated unit groups of modular group algebras. For this, we use Lie and radical algebra methods.