Displaying similar documents to “Fitting height of A -nilpotent groups”

Finite groups with an automorphism of prime order whose fixed points are in the Frattini of a nilpotent subgroup

Anna Luisa Gilotti (1990)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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In this paper it is proved that a finite group G with an automorphism α of prime order r, such that C G α = 1 is contained in a nilpotent subgroup H, with H , r = 1 , is nilpotent provided that either H is odd or, if H is even, then r is not a Fermât prime.

Solvable finite groups with a particular configuration of Fitting sets

Daniela Bubboloni (1995)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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A Fitting set is called elementary if it consists of the subnormal subgroups of the conjugates of a given subgroup. In this paper we analyse the structure of the finite solvable groups in which every Fitting set is the insiemistic union of elementary Fitting sets whose intersection is the subgroup 1.

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...

On locally finite minimal non-solvable groups

Ahmet Arıkan, Sezgin Sezer, Howard Smith (2010)

Open Mathematics

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In the present work we consider infinite locally finite minimal non-solvable groups, and give certain characterizations. We also define generalizations of the centralizer to establish a result relevant to infinite locally finite minimal non-solvable groups.