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The influence of weakly-supplemented subgroups on the structure of finite groups

Qingjun KongQingfeng Liu — 2014

Czechoslovak Mathematical Journal

A subgroup H of a finite group G is weakly-supplemented in G if there exists a proper subgroup K of G such that G = H K . In the paper it is proved that a finite group G is p -nilpotent provided p is the smallest prime number dividing the order of G and every minimal subgroup of P G ' is weakly-supplemented in N G ( P ) , where P is a Sylow p -subgroup of G . As applications, some interesting results with weakly-supplemented minimal subgroups of P G ' are obtained.

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