Abstract
In this paper, we mainly investigate the conjugation of the sylowizer that was introduced by Gaschütz (Math Z 122(4):319–320, 1971) and study the p-supersolvability of finite groups by analyzing the intersection between \(O^{p}(G)\) and sylowizers of p-subgroups. As a continuation of research (Lei and Li in Arch Math (Basel) 114:367–376, 2020), we also give some characterizations on p-nilpotent groups by using the permutability of a sylowizer of a p-subgroup.
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Acknowledgements
We would like to thank the reviewers for their valuable comments towards improving our manuscript. The corresponding author Jia Zhang would like to give sincere gratitude to professor Xiang Li, Chiba University, for offering a research cooperation opportunity.
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To commemorate the 100th birthday of Professor Wolfgang Gaschütz
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This research is supported by the grant of NSFC (Grants # 12001436, 11871058) and Chunhui Plan Cooperative Scientific Research Project of Ministry of Education of the People’s Republic of China and the Fundamental Research Funds of China West Normal University (Grants # 17E091, 18B032).
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Li, X., Zhang, J. On sylowizers in finite groups proposed by Wolfgang Gaschütz. Arch. Math. 116, 251–259 (2021). https://doi.org/10.1007/s00013-020-01553-1
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DOI: https://doi.org/10.1007/s00013-020-01553-1