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具有二元生成的交换极大子群的有限p群
Finite p-groups Which Has Abelian Maximal Subgroup Generated by Two Elements
【摘要】 设G是有限非交换p群.若G中存在一个生成元个数最小是n的交换极大子群,则称G为Mn群.对于p=2,M2群已被分类.对于奇素数p,本文给出了M2群的同构分类,从而M2群被完全分类.
【Abstract】 Assume that G is a finite non-abelian p-group.If G has an abelian maximal subgroup whose number of generators is at least n,then G is called a Mn-group.For p=2.M2-groups have been classified.For p odd prime,M2-groups are classified in this paper,and hence M2-groups are completely classified.
【关键词】 有限p群;
正则p群;
交换极大子群;
生成元个数;
【Key words】 finite p-group; regular p-group; abelian maximal subgroup; number of generator;
【Key words】 finite p-group; regular p-group; abelian maximal subgroup; number of generator;
【基金】 国家自然科学基金(No.11901364);山西省高等学校科技创新项目(No.2020L0613);晋中学院教学改革创新项目(No.Jg202043)
- 【文献出处】 数学进展 ,Advances in Mathematics(CHINA) , 编辑部邮箱 ,2023年04期
- 【分类号】O152.1
- 【下载频次】11