相对M-特征标的替换引理

The Replacement Lemma on Relative M-Characters

摘要: 本文主要目的是将M-特征标的替换引理推广到相对M-特征标的情形，证明了如果 均为有限群G的正规子群使得K/L为奇数阶交换群，则G的每个关于L的相对M-特征标也是关于K的相对M-特征标。特别地，如果G为M-群且K为G的一个奇数阶亚交换正规子群，则G也是关于K的相对M-群。

Abstract: The main goal of the present paper is to generalize the replacement lemma on M-characters to the relative M-characters. It is proved that if are normal subgroups of a finite group G such that K/L is commutative of odd order, then every relative M-character of G with respect to L is also a relative M-character with respect to K. In particular, if G is an M-group with a meta-commutative normal subgroup K of odd order, then G is a relative M-group with respect to K.