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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.

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