两种子群特性与有限群的超可解性  

Two Characteristics of Subgroups and the Supersolvability of Finite Groups

作　　者：石向东[1] 韦华全[2] 谢芬芳[2] 

机构地区：[1]梧州学院数理系,广西梧州543002 [2]广西师范学院数学科学学院,广西南宁530023

出　　处：《广西师范学院学报（自然科学版）》2012年第1期5-8,共4页Journal of Guangxi Teachers Education University(Natural Science Edition)

基　　金：国家自然科学基金(10961007;11161006);广西自然科学基金(0991101);广西教育厅科研基金(200807LX432;00911MS145)

摘　　要：证明了:(1)设G是有限p-可解群,P∈Sylp(G),则G是p-超可解当且仅当P的极大子群在G中半覆盖-远离或G-半置换.(2)有限群G为超可解当且仅当对于G的每个素因子p,存在P∈Sylp(G)使得P的极大子群都在G中半覆盖-远离或PFp(G)-半置换.(3)设F是包含超可解群系的饱和群系,G是有限群,H G使得G/H∈F.如果对于H的任意素因子p,存在P∈Sylp(H)使得P的极大子群都在G中半覆盖-远离或PFp(H)-半置换,则G∈F.The following results were proved：（1） Let G be finite p-solvable group and let P∈Sylp（G）.Then G is p-supersolvable if and only if every maximal subgroup of P is either semi-cover-avoiding or G-semipermutable in G.（2） A finite groups is supersolvable if and only if for every prime divisor of ｜G｜,there exists P∈Sylp（G） such that every maximal subgroup of P is either semi-cover-avoiding or PFp（G）-semipermutable in G.（3） Let F be a saturated formation containing the class of supersolvable groups,G a finite group and H■G such that G/H∈F.If for every prime divisor of ｜H｜,there exists P∈Sylp（H） such thatevery maximal subgroup of P is either semi-cover-avoiding or PFp（H）-semipermutable in G,then G∈F.

关 键 词：有限群 超可解群 半覆盖-远离子群 X-置换 饱和群系 

分 类 号：O152[理学—数学]