特征标公式在有限群的应用

Application of character formula in finite group

摘要

将特征标公式的应用推广到二面体群D_2n和群GL₂(F_p),所得结论如下:当n为奇数时,正规子群＜a＞中只有主特征标可以扩张到群D_2n;群SL₂(F_p)中只有p-1个不可约特征标扩张到群GL₂(F_p).

Abstract

This paper extended the application of character formula to dihedral group D_2n and GL₂(F_p). The conclusion is as follows: if n is odd, only the principal character in normal subgroup ＜a＞ can extend to D_2n, and there are exactly p-1 irreducible characters of SL₂(F_p) that extend to GL₂(F_p).

关键词

二面体群 / 一般线性群 / 特征标扩张

Key words

dihedral group / general linear group / character extension

参考文献

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