Periodic Locally Compact Groups: A Study of a Class of Totally Disconnected Topological Groups

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Wolfgang Herfort Karl H. Hofmann

Periodic Locally Compact Groups

A Study of a Class of Totally Disconnected Topological Groups

Wolfgang Herfort, Karl H. Hofmann, Francesco G. Russo

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English

De Gruyter
19 November 2018

Algebra; Groups & group theory

Series: De Gruyter Studies in Mathematics

This authoritative book on periodic locally compact groups is divided into three parts: The first part covers the necessary background material on locally compact groups including the Chabauty topology on the space of closed subgroups of a locally compact group, its Sylow theory, and the introduction, classifi cation and use of inductively monothetic groups.

The second part develops a general structure theory of locally compact near abelian groups, pointing out some of its connections with number theory and graph theory and illustrating it by a large exhibit of examples.

Finally, the third part uses this theory for a complete, enlarged and novel presentation of Mukhin’s pioneering work generalizing to locally compact groups Iwasawa’s early investigations of the lattice of subgroups of abstract groups.

Contents

Part I: Background information on locally compact groups

Locally compact spaces and groups

Periodic locally compact groups and their Sylow theory

Abelian periodic groups

Scalar automorphisms and the mastergraph

Inductively monothetic groups

Part II: Near abelian groups

The definition of near abelian groups

Important consequences of the definitions

Trivial near abelian groups

The class of near abelian groups

The Sylow structure of periodic nontrivial near abelian groups and their prime graphs

A list of examples

Part III: Applications

Classifying topologically quasihamiltonian groups

Locally compact groups with a modular subgroup lattice

Strongly topologically quasihamiltonian groups

By: Wolfgang Herfort, Karl H. Hofmann, Francesco G. Russo
Imprint: De Gruyter
Country of Publication: Germany
Volume: 71
Dimensions: Height: 240mm, Width: 170mm, Spine: 21mm
Weight: 738g
ISBN: 9783110598476
ISBN 10: 3110598477
Series: De Gruyter Studies in Mathematics
Pages: 354
Publication Date: 19 November 2018
Audience: Professional and scholarly , Undergraduate , Undergraduate
Format: Hardback
Publisher's Status: Active

Wolfgang Herfort, TU Wien, Austria; Karl H. Hofmann, TU Darmstadt, Germany; Francesco G. Russo, University of Cape Town, South Africa.