Abstract
Let G be a finite group. A subgroup H of G is said to be SS-quasinormal in G if there is a subgroup K such that \(G=HK\) and \(HS=SH\), for all \(S\in \) Syl(K), where Syl(K) denotes the collection of all Sylow subgroups of K. A subgroup H of G is said to be SS-supplemented in G if there is a subgroup K such that \(G=HK\) and \(H\cap K\) is SS-quasinormal in G. In this paper, we investigate the SS-supplemented subgroups and strengthen a result of Skiba which gives a positive answer to an open question of Shemetkov.
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Acknowledgements
The authors are grateful to the referee and the editor who provided valuable suggestions and help. In particular, the authors are grateful to the referee, who provided a detailed report and drew our attention to the results in [3].
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Communicated by A. Constantin.
The project is supported by the NSFC (No. 11301532 and 11401116).
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Yan, Q., Bao, X. & Shen, Z. Finite groups with SS-supplement. Monatsh Math 184, 325–333 (2017). https://doi.org/10.1007/s00605-016-1011-0
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DOI: https://doi.org/10.1007/s00605-016-1011-0