| 一系列新的LA-群及其自同构群的阶 |
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| 引用本文： | 班桂宁,张中健,张玉,吴建平. 一系列新的LA-群及其自同构群的阶[J]. 广西科学, 2009, 16(1): 1-3 |
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| 作者姓名： | 班桂宁 张中健 张玉 吴建平 |
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| 作者单位： | 广西大学数学与信息科学学院,广西南宁,530004;广西大学数学与信息科学学院,广西南宁,530004;广西大学数学与信息科学学院,广西南宁,530004;广西大学数学与信息科学学院,广西南宁,530004 |
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| 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 ｜a1^p^t1=a2^p^t2=a3^p^t3=a^p4^t4=…=an^p^tn=1,[a1,a3]=a1^ps,[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.
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| 关 键 词： | 有限p-群 LA-群 自同构群 |
| 收稿时间： | 2008-05-20 |
A New Series of LA-Groups and the Order of Their Automorphism Groups |
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| BAN Gui-ning,ZHANG Zhong-jian,ZHANG Yu and WU Jian-pi. A New Series of LA-Groups and the Order of Their Automorphism Groups[J]. Guangxi Sciences, 2009, 16(1): 1-3 |
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| Authors: | BAN Gui-ning ZHANG Zhong-jian ZHANG Yu WU Jian-pi |
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| Affiliation: | School of Mathematics and Information Sciences;Guangxi University;Nanning;Guangxi;530004;China |
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| Abstract: | 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. |
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| Keywords: | finite p-group LA-group automorphism group |
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