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Czechoslovak Mathematical Journal

, Volume 65, Issue 2, pp 427–433 | Cite as

On solvability of finite groups with some ss-supplemented subgroups

  • Jiakuan Lu
  • Yanyan Qiu
Article
  • 75 Downloads

Abstract

A subgroup H of a finite group G is said to be ss-supplemented in G if there exists a subgroup K of G such that G = HK and HK is s-permutable in K. In this paper, we first give an example to show that the conjecture in A.A. Heliel’s paper (2014) has negative solutions. Next, we prove that a finite group G is solvable if every subgroup of odd prime order of G is ss-supplemented in G, and that G is solvable if and only if every Sylow subgroup of odd order of G is ss-supplemented in G. These results improve and extend recent and classical results in the literature.

Keywords

ss-supplemented subgroup solvable group supersolvable group 

MSC 2010

20D10 20D20 

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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2015

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsGuangxi Normal UniversityGuilinGuangxi, P.R. China

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