摘要
设有限群Ｇ的一切共轭类为ε１，ε２，…，εｔ；ｘｉ∈εｉ（ｉ＝１，２，…，ｔ）．把它们按基数大小顺序排列：｜ε１｜≤｜ε２｜≤…≤｜εｔ｜．设ｍ是使得｜ε１｜＋｜ε２｜＋…＋｜εｍ｜≥｜ＣＧ（ｘｍ）｜的最小正整数．Ｂｅｒｔｒａｎ曾证明：对Ｇ的任一Ａｂｅｌ子群Ａ，均有本文证明了：当Ａ是非Ａｂｅｌ群Ｇ的极大子群且Ａ循环时，Ａ使得（＊）式中等号成立的充要条件是．
Let ε1, ε2, … , εt be all conjugate classes in a finite group G, xi∈εi(i=1, 2, … ,t) and |ε1|≤|ε2|≤…≤|εt| . Suppose m is the minimal positive integer such that E. A. Bertran has proved that for any abelian subgroup A of G.In this paper we prove that if A is a maximal subgroup of G(G nonabelian) and A cyclic then the equality sign holds if and only if
出处
《西南师范大学学报（自然科学版）》
CAS
CSCD
1994年第2期134-138,共5页
Journal of Southwest China Normal University(Natural Science Edition)
关键词
共轭类
有限群
阿贝尔子群
群的阶
conjugate class
finite group
abelian subgroup
the order of group
