Abstract
Let G be a finite group. A subgroup H of G is called s-permutable in G if it permutes with every Sylow subgroup of G, and G is called a PS-group if all minimal subgroups and cyclic subgroups with order 4 of G are s-permutable in G. In this paper, we give a complete classification of finite groups which are not PS-groups but their proper subgroups are all PS-groups.
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Acknowledgements
The authors express their deep sense for gratitude to the anonymous referee for his/her valuable suggestions and comments which refined this paper, and also for providing a concise and original proof for Lemma 2.4. This work was supported by the National Natural Science Foundation of China (No. 11371237), Jiangsu Overseas Research & Training Program for University Prominent Young & Middle-Aged Teachers and Presidents, Qing Lan Project of Jiangsu Province, ‘333’ Project of Jiangsu Province.
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GUO, P., WANG, J. & ZHANG, H. A complete classification of minimal non-PS-groups. Proc Math Sci 124, 511–516 (2014). https://doi.org/10.1007/s12044-014-0195-2
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DOI: https://doi.org/10.1007/s12044-014-0195-2