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浙江大学学报（理学版）
浙江大学学报（理学版）  2019, Vol. 46 Issue (6): 656-659    DOI: 10.3785/j.issn.1008-9497.2019.06.002
数学与计算机科学     
P2-阶子群X-ss-半置换的有限群
谢凤艳
安阳学院 数理学院， 河南安阳 455000
Finite groups with X-ss- semipermutable subgroups of order p2
XIE Fengyan
School of Mathematics and Science，Anyang University，Anyang 455000，Henan Province，China
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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。
关键词： 有限群;  X-ss-半置换子群;  p-幂零群;  p2-阶子群    
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.
Key words: finite group    X-ss-semipermutable subgroups    p-nilpotent group    subgroups of order p2
收稿日期: 2017-05-16 出版日期: 2019-11-25
CLC:  O152.1  
基金资助: 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).
作者简介: 谢凤艳（1984-），ORCID:http://orcid.org/0000-0003-0273-7383,女，硕士，副教授，主要从事有限论研究，E-mail：kfxiefengyan@163.com.
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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）, 2019, 46(6): 656-659.

XIE Fengyan. Finite groups with X-ss- semipermutable subgroups of order p2. Journal of Zhejiang University (Science Edition), 2019, 46(6): 656-659.

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https://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2019.06.002    或    https://www.zjujournals.com/sci/CN/Y2019/V46/I6/656

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