几乎M-可补子群对两类拟F-群结构的影响
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摘要
设G是有限群,E■G.分别考虑E的Sylowp-子群P(其中p是|E|的极小素因子)、E或F~*(E)的非循环Sylowp-子群P,利用其极大子群的几乎M-可补性质,研究了p-拟超可解群、拟超可解群这两类可解饱和群系的结构,得到了一些充分条件.
Let G be a finite group and Ea normal subgroup of G.Some sufficient conditions about p-quasisupersoluble groups and quasisupersoluble groups were obtained by using the nearly M-supplementation of the maximal subgroup of P,in which P was a Sylow p-subgroup of E,where p was the smallest prime divisor of |E| or the non-cyclic Sylow p-subgroup of Eor F~*(E),respectively.
Let G be a finite group and Ea normal subgroup of G.Some sufficient conditions about p-quasisupersoluble groups and quasisupersoluble groups were obtained by using the nearly M-supplementation of the maximal subgroup of P,in which P was a Sylow p-subgroup of E,where p was the smallest prime divisor of |E| or the non-cyclic Sylow p-subgroup of Eor F~*(E),respectively.
引文
[1]徐明曜.有限群导引(上)[M].北京:科学出版社,2007.
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[4]MIAO L,LEMPKEN W.On M-supplemented subgroups of finite groups[J].J Group Theory,2009,12(2):271-287.
[5]WANG Y M,GUO W B.Nearly s-normality of groups and its properties[J].Comm Algebra,2010,38(10):3821-3836.
[6]GUO J D,ZHANG J,MIAO L.On nearly M-supplemented subgroups of finite groups[J].Ukrainian Math J,2014,66(1):66-76.
[7]王强.几乎M-可补子群及其性质[D].扬州:扬州大学数学科学学院,2012.
[8]邱婷婷,王强,鲍宏伟.子群的几乎M-可补子群对群构造的影响[J].江苏师范大学学报(自然科学报),2012,30(3):1-3.
[9]王克科,汤菊萍.子群的几乎M-可补性与p-幂零性[J].扬州大学学报(自然科学报),2014,17(2):1-3,7.
[10]LI S R,HE X L.On normal embedded subgroups of prime power order in finite groups[J].Comm Algebra,2008,36(6):2333-2340.
[11]HUPPERT B,BLACKBURN N.Finite groups III[M].Berlin:Springer-Verlag,1982.
[12]SKIBA A N.A characterization of the hypercyclically embedded subgroups of finite groups[J].J Pure Appl Algebra,2011,215(3):257-261.
[2]GUO W B,SKIBA A N.On some class of finite quasi-F-groups[J].J Group Theory,2009,12(3):407-417.
[3]GUO W B,SKIBA A N.On quasisupersoluble and p-quasisupersoluble finite groups[J].Algebra Colloq,2010,17(4):549-556.
[4]MIAO L,LEMPKEN W.On M-supplemented subgroups of finite groups[J].J Group Theory,2009,12(2):271-287.
[5]WANG Y M,GUO W B.Nearly s-normality of groups and its properties[J].Comm Algebra,2010,38(10):3821-3836.
[6]GUO J D,ZHANG J,MIAO L.On nearly M-supplemented subgroups of finite groups[J].Ukrainian Math J,2014,66(1):66-76.
[7]王强.几乎M-可补子群及其性质[D].扬州:扬州大学数学科学学院,2012.
[8]邱婷婷,王强,鲍宏伟.子群的几乎M-可补子群对群构造的影响[J].江苏师范大学学报(自然科学报),2012,30(3):1-3.
[9]王克科,汤菊萍.子群的几乎M-可补性与p-幂零性[J].扬州大学学报(自然科学报),2014,17(2):1-3,7.
[10]LI S R,HE X L.On normal embedded subgroups of prime power order in finite groups[J].Comm Algebra,2008,36(6):2333-2340.
[11]HUPPERT B,BLACKBURN N.Finite groups III[M].Berlin:Springer-Verlag,1982.
[12]SKIBA A N.A characterization of the hypercyclically embedded subgroups of finite groups[J].J Pure Appl Algebra,2011,215(3):257-261.