一系列新的LA-群及其自同构群的阶  

A New Series of LA-Groups and the Order of Their Automorphism Groups

作　　者：班桂宁[1] 张中健[1] 张玉[1] 吴建平[1] 

机构地区：[1]广西大学数学与信息科学学院

出　　处：《广西科学》2009年第1期1-3,共3页Guangxi Sciences

基　　金：国家自然科学基金项目(NO.60574052)资助

摘　　要：利用循环群扩张理论构造出一系列新群G=〈a1,a2,a3,a4,…,an a1pt1=a2pt2=a3pt3=ap4t4=…=anptn=1,[a1,a3]=a1ps,[ai,aj]=1〉(这里i,j=1,2,…,n,但是i=1,j=3不同时出现在[ai,aj]=1中,p为奇素数,s为整数).给出新群的部分性质及其自同构群的阶,并证明新群均为LA-群.A new series of groups G by extension theory of cyclic group are constructed, whereG=〈a1,a2,a3,a4,…,an ｜a1^p^t1=a2^p^t2=a3^p^t3=a^p4^t4=…=an^p^tn=1,[a1,a3]=a1^ps,[ai,aj]=1〉（i,j=1,2, …, n. In the formula [ai,aj]=1, i=1 and j=3 don＇t occur at the same time, p is an odd prime,s is a positive integer）. We give their properties as well as the order of their automorphism group, and prove that they are all LA-groups.

关 键 词：有限P-群 LA-群 自同构群 

分 类 号：O152.1[理学—数学]