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Covering a group with isolators of finitely many subgroups

Published online by Cambridge University Press:  18 May 2009

Patrizia Longobardi ,
Mercede Maj  and
Akbar H. Rhemtulla
Patrizia Longobardi
Affiliation:
Dlpartimento di Matematica e ApplicazioniUniversita degli Studi di Napolivia Cinthia, Monte S. Angelo80126 Naples– Italy
Mercede Maj
Affiliation:
Dlpartimento di Matematica e ApplicazioniUniversita degli Studi di Napolivia Cinthia, Monte S. Angelo80126 Naples– Italy
Akbar H. Rhemtulla
Affiliation:
Dept. of MathematicsUniversity of AlbertaEdmonton, AlbertaCanada T6G 2G1
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Abstract

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In [6] B. H. Neumann proved the following beautiful result: if a group G is covered by finitely many cosets, say G = xiHi, then we can omit from the union any xiHi, for which |G|Hj| is infinite. In particular, |G:Hj| is finite, for some j ∈ {l,…,n}.

In an unpublished result R. Baer characterized the groups covered by finitely many abelian subgroups, they are exactly the centre-by-finite groups [8]. Coverings by nilpotent subgroups or by Engel subgroups and by normal subgroups have been studied, for example, by R. Baer (see [8]), L. C. Kappe [2,1], M. A. Brodie and R. F. Chamberlain [1], and recently by M. J. Tomkinson [9].

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 35 , Issue 2 , May 1993 , pp. 253 - 259
Copyright
Copyright © Glasgow Mathematical Journal Trust 1993

References

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