English | ISBN: 3110598477 | 2018 | 354 pages | PDF | 5 MB
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.
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