Abstract
In this note, we investigate the influence of pronormal p-subgroups on the structure of finite groups. We not only simplify, but also generalize some main results of Liu et al. (J Algebra Appl 19:2050110, 2020), Shen et al. (Monatshefte Math 175:629–638, 2014) and Yu and Lai (Monatshefte Math 181:745–747, 2016). We also prove that for p-subgroups of finite groups, the concept of pronormal subgroups, weakly normal subgroups and weakly closed subgroups are equivalent.
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Acknowledgements
Haoran Yu is supported by China Postdoctoral Science Foundation (Grant Nos. 2018M630317 and 2019T120231), The Science and Technology Department Project of Jilin Province (Grant No. 20190103029JH), and National Natural Science Foundation of China (Grant Nos. 12001225, 11871241 and 11771176).
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Communicated by John S. Wilson.
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Liu, S., Yu, H. A note on pronormal p-subgroups of finite groups. Monatsh Math 195, 173–176 (2021). https://doi.org/10.1007/s00605-020-01481-w
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DOI: https://doi.org/10.1007/s00605-020-01481-w