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Let G be a finite group of order ( and different primes) such that no different coniugacy classes of G have the same cardinality. Then G is the symmetric group on three letters.
In this paper it is proved that a finite group G with an automorphism of prime order r, such that is contained in a nilpotent subgroup H, with , is nilpotent provided that either is odd or, if is even, then r is not a Fermât prime.
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.
In this Note the Authors study normally embedded subgroups of finite -soluble groups using Fitting sets and generalize results of Anderson [3].
In this Note conditions for the existence of a normal -complement and for the supersolubility of a finite group are given.
In this Note conditions for the existence of a normal -complement and for the supersolubility of a finite group are given.
Nella Nota gli autori danno una nuova condizione necessaria e sufficiente per l’esistenza di -complementi di Sylow normali nei gruppi finiti.
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