On three lattices that belong to every semigroup
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.
We show that any block of a group algebra of some finite group which is of wild representation type has many families of stable tubes.
Assume that S is a commutative complete discrete valuation domain of characteristic p, S* is the unit group of S and is a finite group, where is a p-group and B is a p’-group. Denote by the twisted group algebra of G over S with a 2-cocycle λ ∈ Z²(G,S*). We give necessary and sufficient conditions for to be of OTP representation type, in the sense that every indecomposable -module is isomorphic to the outer tensor product V W of an indecomposable -module V and an irreducible -module...
Let be the ring of p-adic integers, the unit group of and a finite group, where is a p-group and B is a p’-group. Denote by the twisted group algebra of G over with a 2-cocycle . We give necessary and sufficient conditions for to be of OTP representation type, in the sense that every indecomposable -module is isomorphic to the outer tensor product V W of an indecomposable -module V and an irreducible -module W.