有限群的可补的Sylow子群（英文）
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摘要
研究Sylow子群的可补性与群结构的关系,得到了一些关于合成因子构造的结果,推广了Heliel的一个结果.
The relationship between the complementability of Sylow subgroups and the structure of a group was considered,and some results about the construction of composition factors were obtained.Further,one of Heliel's results is the corollary of our results.
The relationship between the complementability of Sylow subgroups and the structure of a group was considered,and some results about the construction of composition factors were obtained.Further,one of Heliel's results is the corollary of our results.
引文
[1]DOERK K,HAWKES T.Finite Soluble Groups[M].Berlin/New York:Walter de Gruyter,1992.
[2]HUPPERT B,BLACKBURN N.Finite GroupsⅢ[M].Berlin/New York:Springer-Verlag,1982.
[3]HALL P.A characteristic property of solvable groups[J].J London Math Soc,1937,12:188-200.
[4]ARAD Z,WARD M B.New criteria for the solvability of finite groups[J].J Algebra,1982,77:234-246.
[5]BALLESTER-BOLINCHES A,GUO X.On complemented subgroups of finite groups[J].Arch Math,1999,72:161-166.
[6]QIAN G,TANG F.Finite groups with certain subgroups of prime power order complemented[J].JAlgebra,2015,423:950-962.
[7]MONAKHOV V S,KNIAHINA V N.Finite groups with complemented subgroups of prime orders[J].JGroup Theory,2015,18:905-912.
[8]ASAAD M.Finite groups with certain subgroups of Sylow subgroups complemented[J].J Algebra,2010,323:1958-1965.(下转第905页)
[9]GURALNICK R.Subgroups of prime power index in a simple group[J].J Algebra,1983,811:304-311.
[10]GUO W.The Theory of Classes of Groups[M].Beijing/New York/Dordrecht/Boston/London:Science Press/Kluwer Academic Publishers,2000.
[11]BUGEAUD Y,CAO Z,MIGNOTTE M.On simple K4-groups[J].J Algebra,2002,241:658-668.
[12]WANG Y.Finite groups with some subgroups of Sylow subgroups c-supplemented[J].J Algebra,2000,224(2):467-478.
[13]HELIEL A A.A note on c-supplemented subgroups of finite groups[J].Comm Algebra,2014,42:1650-1656.
[2]HUPPERT B,BLACKBURN N.Finite GroupsⅢ[M].Berlin/New York:Springer-Verlag,1982.
[3]HALL P.A characteristic property of solvable groups[J].J London Math Soc,1937,12:188-200.
[4]ARAD Z,WARD M B.New criteria for the solvability of finite groups[J].J Algebra,1982,77:234-246.
[5]BALLESTER-BOLINCHES A,GUO X.On complemented subgroups of finite groups[J].Arch Math,1999,72:161-166.
[6]QIAN G,TANG F.Finite groups with certain subgroups of prime power order complemented[J].JAlgebra,2015,423:950-962.
[7]MONAKHOV V S,KNIAHINA V N.Finite groups with complemented subgroups of prime orders[J].JGroup Theory,2015,18:905-912.
[8]ASAAD M.Finite groups with certain subgroups of Sylow subgroups complemented[J].J Algebra,2010,323:1958-1965.(下转第905页)
[9]GURALNICK R.Subgroups of prime power index in a simple group[J].J Algebra,1983,811:304-311.
[10]GUO W.The Theory of Classes of Groups[M].Beijing/New York/Dordrecht/Boston/London:Science Press/Kluwer Academic Publishers,2000.
[11]BUGEAUD Y,CAO Z,MIGNOTTE M.On simple K4-groups[J].J Algebra,2002,241:658-668.
[12]WANG Y.Finite groups with some subgroups of Sylow subgroups c-supplemented[J].J Algebra,2000,224(2):467-478.
[13]HELIEL A A.A note on c-supplemented subgroups of finite groups[J].Comm Algebra,2014,42:1650-1656.