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

Periodic Locally Compact Groups

A Study of a Class of Totally Disconnected Topological Groups

Series:De Gruyter Studies in Mathematics 71

    103,95 € / $119.99 / £94.50*

    eBook (EPUB)
    Publication Date:
    November 2018
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    • An authoritative monograph on locally compact periodic groups
    • Written by well-known experts in the field
    • Of interest to researchers and graduate students in group theory and algebra

    Aims and Scope

    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


    liii, 301 pages
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    Wolfgang Herfort, TU Wien, Austria; Karl H. Hofmann, TU Darmstadt, Germany; Francesco G. Russo, University of Cape Town, South Africa.

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