Abstract: In this paper we obtain various sufficient conditions for the solubility of a finite group. In particular, we show that if G is a finite group and p ≥5 is a prime such that all p′ -subgroups of G are nilpotent, then G is soluble. We show also that if G is a finite group which has a cyclic Sylow p -subgroup P and such that for all p′ -subgroups H of G, H is nilpotent and H′ is cyclic, then, if p ≠3, either P ◃ G or G has a normal p -complement.
Publication Year: 1973
Publication Date: 1973-01-01
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 2
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