Primitive characters of maximal subgroups of solvable groups
Primitive characters of maximal subgroups of solvable groups
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DOI：
10.1016/j.jalgebra.2009.05.033
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发表时间：
2010-01
影响因子：
0.9
通讯作者：
I. Isaacs;Tom Wilde
中科院分区：
文献类型：
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作者：
I. Isaacs;Tom Wilde
设G是M-群，H是奇指标的极大子群，β∈irrH是本原的。Mark Lewis证明了β(1)2除以|G：H|。在这种情况下，我们证明了β(1)2=|G：H|或β(1)=1。对于不一定是M-群的群，建立了一些相关的结果。
Let G be an M-group, and suppose that H is a maximal subgroup of odd index and that β∈IrrH is primitive. It was shown by Mark Lewis that β(1)2divides |G:H|. We show in this situation that either β(1)2=|G:H| or β(1)=1. A number of related results are established for groups that are not necessarily M-groups.