摘要
群Ｇ的子群Ｈ称为是Ｇ的半正规子群，若对任意Ｇ的子群Ｋ，只要Ｋ的阶数与Ｈ互质，则Ｈ与Ｋ可置换；称Ｈ在Ｇ中是反正规的，若对任意ｇ∈Ｇ，ｇ，∈＜Ｈ．Ｈｇ＞．本文刻画了每个子群是半正规的，或反正规的有限群，推广了［１］及［２］中的结果．
A subgroup H of a group G is called seminormal in G if H permutes with all subgroups K of G of order prime to H ; and H is called abnormal in G if g ∈<H. H9> for all g in G. In this paper, we study and characterize those finite groups in which every subgroup is either seminormal or abnormal, and the results of paper [1] and [2] are generalized.
出处
《数学研究》
CSCD
1996年第4期10-15,共6页
Journal of Mathematical Study
关键词
反正规子群
有限群
半正规子群
幂自同构
seminormal subgroup, abnormal subgroup, power automorphism, nilpotent residual
