Journal of Guangxi Normal University(Natural Science Edition) ›› 2017, Vol. 35 ›› Issue (1): 49-52.doi: 10.16088/j.issn.1001-6600.2017.01.008

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The Influence of Weakly s-supplemented Subgroups on Solvability of Finite Groups

LU Jiakuan, QIU Yanyan   

  1. College of Mathematics and Statistics, Guangxi Normal University, Guilin Guangxi 541004, China
  • Online:2017-01-20 Published:2018-07-17

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Abstract: A subgroup H of a finite group G is called weakly s-supplemented subgroup of G if there is a subgroup K of G such that G=HK and H∩K≤HsG, where HsG is the subgroup of H generated by all those subgroups of H which are s-permutable in G. In this paper, the following results are proved: (1) a finite group G is solvable if every subgroup of odd prime order of G is weakly s-supplemented in G; (2) a finite group G is solvable if and only if every Sylow subgroup of odd order of G is weakly s-supplemented in G. Some classical and recent results are extended.

Key words: weakly s-supplemented subgroup, solvable group, supersolvable group

CLC Number: 

  • O152.1
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