| P2-阶子群X-ss-半置换的有限群 |
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| 引用本文： | 谢凤艳.P2-阶子群X-ss-半置换的有限群[J].浙江大学学报(理学版),1959,46(6):656-659. |
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| 作者姓名： | 谢凤艳 |
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| 基金项目： | 河南省高等学校青年骨干教师培养计划（2016GGJS-204);安阳学院科研培育基金项目（2018-AYPYJJZD-006). |
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| 摘 要： | 设G是有限群，X是G的一个非空子集，子群H称为在G中X-ss-半置换，若H在G中有补充子群T，对于T的任意Sylowp-子群P，只要(p,|H|)=1，就存在x∈X使得HPx=PxH。通过对p2-阶子群的X-ss-半置换性研究，得到了p-幂零群的新判断。
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| 关 键 词： | 有限群 X-ss-半置换子群 p-幂零群 p2-阶子群 |
| 收稿时间： | 2017-05-16 |
Finite groups with X-ss- semipermutable subgroups of order p2 |
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| XIE Fengyan.Finite groups with X-ss- semipermutable subgroups of order p2[J].Journal of Zhejiang University(Sciences Edition),1959,46(6):656-659. |
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| Authors: | XIE Fengyan |
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| Institution: | School of Mathematics and Science，Anyang University，Anyang 455000，Henan Province，China |
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| Abstract: | Let G be a finite group and Xbe a nonempty subset of G. A subgroup H of G is said to be X-ss-semipermutable in G if H has a supplement T in G, such that H is X-permutable with every Sylow p-subgroups of T with (p,|H|)=1. By investigating X-ss-semipermutability of some subgroups of order p2, some criteria of p-nilpotency of finite groups are obtained. |
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| Keywords: | finite group X-ss-semipermutable subgroups p-nilpotent group subgroups of order p2 |
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