一类非交换群的自同态和自同构数量  

The number of endomorphisms and automorphisms of a class of non-abelian groups

作　　者：张维 郭继东 张良 ZHANG Wei;GUO Ji-dong;ZHANG Liang(College of Mathematics and Statistics,Yili Normal University,Yining 835000,Xinjiang,China;Institute of Applied Mathematics,Yili Normal University,Yining 835000,Xinjiang,China)

机构地区：[1]伊犁师范大学数学与统计学院,新疆伊宁835000 [2]伊犁师范大学应用数学研究所,新疆伊宁835000

出　　处：《山东大学学报（理学版）》2023年第2期13-19,共7页Journal of Shandong University(Natural Science)

基　　金：新疆维吾尔自治区高校科研计划自然科学重点项目(XJEDU2020I018)。

摘　　要：基于群理论下一类非交换群的群结构以及元素的阶,计算一类Sylow p-子群为循环群的2qp^(n)(q<p为奇素数)阶非交换群的自同态个数和自同构个数,并验证其自同态个数满足T.Asai和T.Yoshida猜想。Based on the group structure and the order of elements of a class of non-abelian groups in group theory,the number of endomorphisms and automorphisms of a class of non-abelian groups of order 2qp^(n)whose Sylow p-subgroups is cyclic is calculated,where q<p and both are odd primes.Moreover,it is proved that the number of endomorphisms of such groups satisfies the conjecture of T.Asai and T.Yoshida in this case.

关 键 词：非交换群 自同态 自同构 T.Asai&T.Yoshida猜想 

分 类 号：O152.6[理学—数学]