有限群的广义交换度  

The Generalized Commutativity Degree of Finite Groups

作　　者：周峰[1] 周芳[2] 刘合国[1] 

机构地区：[1]湖北大学数学系,武汉430062 [2]太原师范学院数学系,太原030619

出　　处：《数学年刊（A辑）》2016年第2期127-136,共10页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.11371124,No.11401424)的资助

摘　　要：给出了有限群广义交换度的一些性质.某种意义下,广义交换度测度了所有子群正规化子阶的平均值.通过考虑一类内交换群,探索了有限群的幂零性(可解性)与其广义交换度之间的关系.对于二面体群及含有循环极大子群的P-群,给出了其广义交换度的详细公式.The authors give some properties of the generalized commutativity degree of finite groups.This quantity measures the mean value of the orders of the normalizes in some sense.Some limits are also obtained to investigate the connection between the nilpotency（solvability） of a finite group G and its generalized commutativity degree by considering certain minimal non-abelian groups.Explicit formulas are obtained for finite dihedral groups and finite p-groups possessing a cyclic maximal subgroup.

关 键 词：交换 P-群 幂零 可解 

分 类 号：O152.1[理学—数学]