Abstract
Let G be a finite group. We say that a subgroup H of G is weakly SΦ-supplemented in G if G has a subgroup T such that G = HT and H∩T ≤ Φ(H)H sG , where H sG is the subgroup of H generated by all those subgroups of H that are s-permutable in G. In this paper, we investigate the influence of weakly SΦ-supplemented subgroups on the structure of finite groups. Some new characterizations of p-nilpotency and supersolubility of finite groups are obtained.
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Original Russian Text Copyright © 2016 Wu Zh., Mao Y., and Guo W.
The authors were supported by the NNSF of China (Grant 11371335) and the Wu Wen-Tsun Key Laboratory of Mathematics of the Chinese Academy of Sciences.
Hefei; Datong. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 57, No. 4, pp. 889–898, July–August, 2016; DOI: 10.17377/smzh.2016.57.411. Original article submitted June 1, 2015.
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Wu, Z., Mao, Y. & Guo, W. On weakly SΦ-supplemented subgroups of finite groups. Sib Math J 57, 696–703 (2016). https://doi.org/10.1134/S003744661604011X
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DOI: https://doi.org/10.1134/S003744661604011X