| 14 | 0 | 10 |
| 下载次数 | 被引频次 | 阅读次数 |
M-群的一个著名问题,M-群的Hall-子群是M-群吗?文章给出了M-群的Hall-子群是M-群的一个充分条件:如果G是M-群,H是G的Hall子群。如果对于任意一个(?)∈Irr(H),都有p(?)(1),则H是M-群。
Abstract：A famous problem of finite groups is that:Hall subgroups of M-groups are M-groups?A sufficient condition tor Hall subgroups of M-groups being M-groups is given in the paper:Suppose that G is M-group with Hall subgroup H and p(?)(1)if every chatacter (?)∈Irr(H),then H is M-group.
[1]丘维声，有限群和紧群的表示论[M]．北京：北京大学出版社，1997．
[2]Dade E C.Nnormal subgroups of M-groups need not be M-groups[J].Math.Z.,1973,133:313-317.
[3]Domhoff L.M-groups and 2-groups[J].Math.Z.,1967,100:226-256.
[4]Fukushima H.Hall subgroups of M-groups need not be M-groups[J].Proc.Amer.Math.Soc.,2004,133(3):671-675.
[5]Huppert B.Character theory of finite groups[M].New York:Springer,1998.
[6]Robinson D J S.A course in the theory of groups 2nd[M].New York:Sprmger-Verlag,1995.
[7]Isaacs I M,Navarro G.Character correspondences and irreducible induction and restriction[J].J.Alg,1991,140(1):131-140.
[8]Isaacs I M.Hall Subgroup nonnalizers and character correspondence in M-groups[J].Proc.Amer.Math.Soc.,1990,109:647-651.
基本信息:
中图分类号:O152
引用信息:
[1]魏水平,刘仕田.M-群的Hall-子群是M-群的一个充分条件[J].四川理工学院学报(自然科学版),2007,No.82(06):36-38.
2007-12-15
2007-12-15