Locally (Soluble-by-Finite) Groups With Various Restrictions on Subgroups of Infinite Rank

Abstract

Abstract. We present some results on locally (soluble-by-finite) groups with various restrictions on subgroups of infinite rank.

Groups with countably many subgroups

“…By the first part of the proof, all locally soluble subgroups of G are soluble, hence of finite rank by Theorem 2.7. Then the main theorem in [5] (also see [6]) shows that G has a locally soluble subgroup of finite index. The result follows.…”