Elliptically embedded subgroups and nilpotent products

Abstract

A recent paper of Rhemtulla and Wilson [4] is concerned with elliptically embedded subgroups of groups. A subgroup H of a group G is elliptically embedded in G if, for each subgroup K of G, there is some integer m such that (H, K) = (HK)m. Some sufficient conditions for elliptic embedding are given in Section 2 of [4], and some consequences of the presence of this property are to be found in Theorems 1 and 2 of the same paper and in the main theorem of [5]. It is evident from all of these results that the property of being elliptically embedded is closely related to the nilpotency and subnormality of certain subgroups. One of the questions considered here i s the following.