Finite groups with some pronormal subgroups |
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| Authors: | Zhen Cai Shen Wu Jie Shi |
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| Affiliation: | [1]School of Mathematical Sciences, Suzhou University, Suzhou 215006, P. R. China [2]School of Mathematics and Statistics, Chongqing University of Arts and Sciences, Chongqing 402160, P. R. China |
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| Abstract: | A subgroup H of finite group G is called pronormal in G if for every element x of G, H is conjugate to H x in 〈H, H x 〉. A finite group G is called PRN-group if every cyclic subgroup of G of prime order or order 4 is pronormal in G. In this paper, we find all PRN-groups and classify minimal non-PRN-groups (non-PRN-group all of whose proper subgroups are PRN-groups). At the end of the paper, we also classify the finite group G, all of whose second maximal subgroups are PRN-groups. |
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| Keywords: | Pronormal subgroups PRN-groups minimal non-PRN-groups PN-groups minimalsubgroups p-nilpotent groups |
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