Properties of a class of groups on class="a-plus-plus">Z _{class="a-plus-plus"> class="a-plus-plus">m}

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• 作者：Benwen Huang ; Li Zhang ; Xiaotao Wu
• 关键词：direct product ; solvable group ; isomorphism ; maximal normal subgroup ; primitive root ; finite simple group
• 刊名：Wuhan University Journal of Natural Sciences
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：22
• 期：1
• 页码：5-12
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Life Sciences, general; Materials Science, general; Computer Science, general;
• 出版者：Wuhan University
• ISSN：1993-4998
• 卷排序：22

文摘

In this paper, we obtain the factorization of direct production and order of group GL(n, Z_m) in a simple method. Then we generalize some properties of GL(2, Z_p) proposed by Huppert, and prove that the group \(GL\left( {2,{Z_{{z^\lambda }}}} \right)\) is solvable. We also prove that group GL(n, Z_p) is solvable if and only if GL(n, Z_p) is solvable, and list the generators of groups GL(n, Z_p) and SL(n, Z_p). At last, we prove that PSL(2, Z_p)(p > 3) and PSL(n, Z_p)(n > 3) are simple.