Displaying similar documents to “On Engel-like congruences”

Groups with many nilpotent subgroups

Patrizia Longobardi, Mercede Maj, Avinoam Mann, Akbar Rhemtulla (1996)

Rendiconti del Seminario Matematico della Università di Padova

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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...

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.