Covering a group with isolators of finitely many subgroups

Abstract

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 In particular, |G:Hj|is finite, for some j∈ {l,…,n}.In an unpublished result R. Baer characterized the groups covered by finitely many abelian subgroups, they are exactly the centre-by-finite groups [8].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].