The influence of X-semipermutability of subgroups on the structure of finite groups |
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| Authors: | GuiYun Chen JinBao Li |
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| Affiliation: | (1) School of Mathematics and Statistics, Southwest University, Chongqing, 400715, China;(2) School of Mathematical Sciences, Xuzhou Normal University, Xuzhou, 221116, China |
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| Abstract: | Let A be a subgroup of a group G and X be a nonempty subset of G. A is said to be X-semipermutable in G if A has a supplement T in G such that A is X-permutable with every subgroup of T. In this paper, we investigate further the influence of X-semipermutability of some subgroups on the structure of finite groups. Some new criteria for a group G to be supersoluble or p-nilpotent are obtained. This work was supported by National Natural Science Foundation of China (Grant Nos. 10771172, 10771180) |
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| Keywords: | finite groups X-semipermutable subgroups supersoluble groups p-nilpotent groups subnormal subgroups Sylow subgroups cyclic subgroups |
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