Permutability in uncountable groups

Abstract

A subgroup X of a group G is called permutable if $$XY=YX$$ for all subgroups Y of G. It is well known that permutable subgroups play an important role in many problems in group theory, and the purpose of this paper is to describe the structure of uncountable groups of regular cardinality $$\aleph $$ in which all large subgroups are permutable.