A note on commutator subgroups in groups of large cardinality

If G is an uncountable group of regular cardinality aleph, we shall denote by LL aleph(G) the set of all subgroups of G of cardinality aleph. The aim of this paper is to describe the behaviour of groups G for which the set C aleph(G)={X '|X is an element of LL aleph(G)} is finite, at least when G is locally graded and has no simple sections of cardinality aleph. Among other results, it is proved that such a group has a finite commutator subgroup, provided that it contains an abelian subgroup of cardinality aleph.