c*-Supplemented subgroups and p-nilpotency of finite groups
c*-Supplemented subgroups and p-nilpotency of finite groups
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DOI：
10.1007/s11253-007-0073-5
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发表时间：
2007-08
影响因子：
0.5
通讯作者：
H. Wei;Y. Wang
中科院分区：
文献类型：
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作者：
H. Wei;Y. Wang
有限群的子群称为*-补充群，如果存在这样的子群g = hkh，则称为*-补充群。证明了一个有限群G isS4-free isp-幂零ifNG(P) isp-幂零，并且对于所有x∈G\NG(P)， isc*-补inP的每一个极小子群（ifp= 2）都满足下列条件之一：(a) isc*-补inP的每一个4阶循环子群，(b), (c) p4元无，其中gandp的sylop -子群是G的P -幂零残差。这扩展并改进了一些已知的结果。
A subgroupHof a finite groupGis said to bec*-supplemented inGif there exists a subgroupKsuch thatG=HKandH⋂Kis permutable inG. It is proved that a finite groupGthat isS4-free isp-nilpotent ifNG(P) isp-nilpotent and, for allx∈G\NG(P), every minimal subgroup ofisc*-supplemented inPand (ifp= 2) one of the following conditions is satisfied: (a) every cyclic subgroup ofof order 4 isc*-supplemented inP, (b), (c)Pis quaternion-free, wherePa Sylowp-subgroup ofGandis thep-nilpotent residual ofG. This extends and improves some known results.