Joins of Almost Subnormal Subgroups

Abstract

Following (1) we say that a subgroup H of a group G is almost subnormal in G if H is of finite index in some subnormal subgroup of G, or, equivalently, if |Hn : H| is finite for some n, where Hn is the n-th term of the normal closure series of H in G. The aim of this article is to prove, in answer to a question of R. Baer, the following analogue of the well known result of Roseblade and Stonehewer (3) that in any group the join of a pair of finitely generated subnormal subgroups is always subnormal: