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Group Rings of Simple Locally Finite Groups

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Finite and Locally Finite Groups

Part of the book series: NATO ASI Series ((ASIC,volume 471))

Abstract

This is an expository paper which describes some new ideas and results on the group rings of simple locally finite groups. The problem of describing the two-sided ideal lattice is restated in terms of the representation theory of finite groups. This leads to various asymptotic problems for representations of finite groups. The problem is also linked with describing permutation representations, satisfying some finiteness condition, of simple locally finite groups. The ground field is mainly of characteristic 0. The modular case is described briefly in the last section.

This work was supported in part by International Science Foundation Grant No. RWXOOO.

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Author notes

  1. A. E. Zalesskiĭ

    Present address: Department of Mathematics, Bilkent University, 06533, Bilkent, Ankara, Turkey

Authors and Affiliations

  1. Institute of Mathematics of the Academy of Sciences of Belaruse, Minsk, 220072, Belaruse

    A. E. Zalesskiĭ

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  1. A. E. Zalesskiĭ
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Editors and Affiliations

  1. Department of Mathematics, University of Manchester, Manchester, UK

    B. Hartley

  2. Department of Mathematics, University of Oregon, Eugene, Oregon, USA

    G. M. Seitz

  3. UMIST, Manchester, UK

    A. V. Borovik  & R. M. Bryant  & 

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Zalesskiĭ, A.E. (1995). Group Rings of Simple Locally Finite Groups. In: Hartley, B., Seitz, G.M., Borovik, A.V., Bryant, R.M. (eds) Finite and Locally Finite Groups. NATO ASI Series, vol 471. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0329-9_9

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  • DOI: https://doi.org/10.1007/978-94-011-0329-9_9

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-4145-4

  • Online ISBN: 978-94-011-0329-9

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