Displaying similar documents to “On complemented subgroups of finite groups”

On subgroups of ZJ type of an F-injector for Fitting classes F between E and ES.

Ana Martínez Pastor (1994)

Publicacions Matemàtiques

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Let G be a finite group and p a prime. We consider an F-injector K of G, being F a Fitting class between E y ES, and we study the structure and normality in G of the subgroups ZJ(K) and ZJ*(K), provided that G verifies certain conditions, extending some results of G. Glauberman (A characteristic subgroup of a p-stable group, (1968), 555-564).

On central nilpotency in finite loops with nilpotent inner mapping groups

Markku Niemenmaa, Miikka Rytty (2008)

Commentationes Mathematicae Universitatis Carolinae

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In this paper we consider finite loops whose inner mapping groups are nilpotent. We first consider the case where the inner mapping group I ( Q ) of a loop Q is the direct product of a dihedral group of order 8 and an abelian group. Our second result deals with the case where Q is a 2 -loop and I ( Q ) is a nilpotent group whose nonabelian Sylow subgroups satisfy a special condition. In both cases it turns out that Q is centrally nilpotent.

On a class of finite solvable groups

James Beidleman, Hermann Heineken, Jack Schmidt (2013)

Open Mathematics

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A finite solvable group G is called an X-group if the subnormal subgroups of G permute with all the system normalizers of G. It is our purpose here to determine some of the properties of X-groups. Subgroups and quotient groups of X-groups are X-groups. Let M and N be normal subgroups of a group G of relatively prime order. If G/M and G/N are X-groups, then G is also an X-group. Let the nilpotent residual L of G be abelian. Then G is an X-group if and only if G acts by conjugation on...