Group Characters and Normal Hall Subgroups
Group Characters and Normal Hall Subgroups
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DOI：
10.1017/s0027763000023849
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发表时间：
1962-12
影响因子：
0.8
通讯作者：
P. Gallagher
中科院分区：
文献类型：
--
作者：
P. Gallagher
1. 引言 设 G 为有限群，ψ 为正规子群 N 的（普通）不可约特征。如果 ψ 扩展到 G 的特征，则 ψ 在 G 下是不变的，反之则成立。第3节表明，如果ψ一致延伸到中间群H，其中H/N是初等群，则ψ延伸到G。如果N是霍尔子群，那么为了使ψ延伸到G，ψ在G下保持不变就足够了。在这种情况下，这导致从N的特征和G/N的子群的特征构造G的特征。
1. Introduction Let G be a finite group and let ψ be an (ordinary) irreducible character of a normal subgroup N. If ψ extends to a character of G then ψ is invariant under G, but the converse is false. In section 3 it is shown that if ψ extends coherently to the intermediate groups H for which H/N is elementary, then ψ extends to G. If N is a Hall subgroup, then in order for ψ to extend to G it is sufficient that ψ be invariant under G. This leads to a construction of the characters of G from the characters of N and the characters of the subgroups of G/N in this case.