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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

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.

p-Injectors and finite supersoluble groups

Anna Luisa GilottiLuigi Serena — 1977

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

In questa Nota gli Autori, proseguendo lo studio iniziato in [2] sui p-iniettori nei gruppi finiti, introducono la definizione di p-1-catena e provano che l'esistenza in un gruppo finito G di p-1-catene per ogni primo p che divide |G| equivale alla supersolubilità di G.

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