On the weak regularity of semigroup rings.
Let be a group. A subgroup of is called a TI-subgroup if or for every and is called a QTI-subgroup if for any . In this paper, a finite group in which every nonabelian maximal is a TI-subgroup (QTI-subgroup) is characterized.
A subgroup H of a group G is inert if |H: H ∩ H g| is finite for all g ∈ G and a group G is totally inert if every subgroup H of G is inert. We investigate the structure of minimal normal subgroups of totally inert groups and show that infinite locally graded simple groups cannot be totally inert.
This article is dedicated to soluble groups, in which pronormality is a transitive relation. Complete description of such groups is obtained.