数学研究
數學研究
수학연구
JOURNAL OF MATHEMATICAL STUDY
2009年
4期
434-440
,共7页
s-半置换子群%极大子群%极小子群%p-超可解群
s-半置換子群%極大子群%極小子群%p-超可解群
s-반치환자군%겁대자군%겁소자군%p-초가해군
s-semipermutable subgroups%maximal subgroups%minimal subgroups%p-supersolvablegroups
群G的子群日称为半置换的,若对任意的K≤G,只要(ㄧHㄧ,ㄧKㄧ)=1,就有HK=KH.H称为s-半置换的.若对任意的pㄧㄧGㄧ,只要(p,ㄧHㄧ)=1,就有PH=HP,其中P∈Syl_p (G).本文研究Sylow子群的极大子群及极小子群的s-半置换性对有限群的p-超可解性的影响.
群G的子群日稱為半置換的,若對任意的K≤G,隻要(ㄧHㄧ,ㄧKㄧ)=1,就有HK=KH.H稱為s-半置換的.若對任意的pㄧㄧGㄧ,隻要(p,ㄧHㄧ)=1,就有PH=HP,其中P∈Syl_p (G).本文研究Sylow子群的極大子群及極小子群的s-半置換性對有限群的p-超可解性的影響.
군G적자군일칭위반치환적,약대임의적K≤G,지요(ㄧHㄧ,ㄧKㄧ)=1,취유HK=KH.H칭위s-반치환적.약대임의적pㄧㄧGㄧ,지요(p,ㄧHㄧ)=1,취유PH=HP,기중P∈Syl_p (G).본문연구Sylow자군적겁대자군급겁소자군적s-반치환성대유한군적p-초가해성적영향.
Let G be a finite group. A subgroup H of a group G is called semipermutable if it is permutable with every subgroup K of G with (|H|,|K|)=1,and s-semipermutable if it is permutable with every Sylow p-subgroup of G with (p,(|H|))=1.The influence of s-semipermutablity of maximal subgroups and minimal subgroups of Sylow subgroup of a finite group on its p-supersolvability are investigated.
