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On TI-subgroups and QTI-subgroups of finite groups

Ruifang Chen, Xianhe Zhao (2020)

Czechoslovak Mathematical Journal

Let G be a group. A subgroup H of G is called a TI-subgroup if H H g = 1 or H for every g G and H is called a QTI-subgroup if C G ( x ) N G ( H ) for any 1 x H . In this paper, a finite group in which every nonabelian maximal is a TI-subgroup (QTI-subgroup) is characterized.

On totally inert simple groups

Martyn Dixon, Martin Evans, Antonio Tortora (2010)

Open Mathematics

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.

On transitivity of pronormality

Leonid A. Kurdachenko, Igor Ya. Subbotin (2002)

Commentationes Mathematicae Universitatis Carolinae

This article is dedicated to soluble groups, in which pronormality is a transitive relation. Complete description of such groups is obtained.

On tubes for blocks of wild type

Karin Erdmann (1999)

Colloquium Mathematicae

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.

On twisted group algebras of OTP representation type

Leonid F. Barannyk, Dariusz Klein (2012)

Colloquium Mathematicae

Assume that S is a commutative complete discrete valuation domain of characteristic p, S* is the unit group of S and G = G p × B is a finite group, where G p is a p-group and B is a p’-group. Denote by S λ G the twisted group algebra of G over S with a 2-cocycle λ ∈ Z²(G,S*). We give necessary and sufficient conditions for S λ G to be of OTP representation type, in the sense that every indecomposable S λ G -module is isomorphic to the outer tensor product V W of an indecomposable S λ G p -module V and an irreducible S λ B -module...

On twisted group algebras of OTP representation type over the ring of p-adic integers

Leonid F. Barannyk, Dariusz Klein (2016)

Colloquium Mathematicae

Let ̂ p be the ring of p-adic integers, U ( ̂ p ) the unit group of ̂ p and G = G p × B a finite group, where G p is a p-group and B is a p’-group. Denote by ̂ p λ G the twisted group algebra of G over ̂ p with a 2-cocycle λ Z ² ( G , U ( ̂ p ) ) . We give necessary and sufficient conditions for ̂ p λ G to be of OTP representation type, in the sense that every indecomposable ̂ p λ G -module is isomorphic to the outer tensor product V W of an indecomposable ̂ p λ G p -module V and an irreducible ̂ p λ B -module W.

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