2017
Том 69
№ 9

All Issues

Weakly SS-Quasinormal Minimal Subgroups and the Nilpotency of a Finite Group

Zhang X., Zhao Tao

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Abstract

A subgroup H is said to be an s-permutable subgroup of a finite group G provided that the equality HP =PH holds for every Sylow subgroup P of G. Moreover, H is called SS-quasinormal in G if there exists a supplement B of H to G such that H permutes with every Sylow subgroup of B. We show that H is weakly SS-quasinormal in G if there exists a normal subgroup T of G such that HT is s-permutable and H \ T is SS-quasinormal in G. We study the influence of some weakly SS-quasinormal minimal subgroups on the nilpotency of a finite group G. Numerous results known from the literature are unified and generalized.

English version (Springer): Ukrainian Mathematical Journal 66 (2014), no. 2, pp 209-217.

Citation Example: Zhang X., Zhao Tao Weakly SS-Quasinormal Minimal Subgroups and the Nilpotency of a Finite Group // Ukr. Mat. Zh. - 2014. - 66, № 2. - pp. 187–194.

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