Abstract
Let G be a finite group. A subgroup H of a group G is called pronormal in G if the subgroups H and \(H^g\) are conjugate in \(\langle H, H^g\rangle \) for each \(g\in G\). A group G is said to be a PRN-group if every minimal subgroup of G or order 4 is pronormal in G. In this paper, we characterize groups G such that G is a non-PRN-group of even order in which every maximal subgroup of even order is a PRN-group, and come to that such groups are solvable, have orders divisible by at most 3 distinct primes. And some additional structural details are provided.
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The authors would like to thank the referee for his/her valuable suggestions and useful comments that contributed to the preparation of the final version of the paper.
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This research was partially supported by Fundamental Research Funds for the Central Universities (No. XDJK2020B052), the National Natural Science Foundation of China (Nos. 11971391, 12071376). Chongqing Natural Science Foundation (cstc2021jcyj-msxm1984) and Teaching Reform Project of Southwest University (2019JY096).
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Chen, K., Liu, J. Finite groups all of whose maximal subgroups of even order are PRN-groups. Ricerche mat 73, 773–780 (2024). https://doi.org/10.1007/s11587-021-00636-7
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DOI: https://doi.org/10.1007/s11587-021-00636-7