特征标公式在有限群的应用

Application of character formula in finite group

将特征标公式的应用推广到二面体群D_(2n)和群GL_(2)(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SL_(2)(F_(p))中只有p-1个不可约特征标扩张到群GL_(2)(F_(p)).

This paper extended the application of character formula to dihedral group D2nand GL_(2)(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-1irreducible characters of SL_(2)(F_(p))that extend to GL_(2)(F_(p)).