40阶群和56阶群的同构分类  

Isomorphic classification of order 40 and order 56 groups

作　　者：李德乐[1] 曹慧芹 LI Dele;CAO Huiqin(Fujian College of Water Conservancy and Electric Power,Yongan 366000,China;School of Mathematical Sciences,Xiamen University,Xiamen 361005,China)

机构地区：[1]福建水利电力职业技术学院公共基础部,福建永安366000 [2]厦门大学数学科学学院,福建厦门361005

出　　处：《厦门大学学报（自然科学版）》2021年第1期58-62,共5页Journal of Xiamen University：Natural Science

基　　金：国家自然科学基金(12071386);福建省中青年教师教育科研项目(JA15796)。

摘　　要：设G是40(即23·5)阶群,P∈Syl2(G),Q∈Syl5(G),本文运用王慧群等的相关结果,以及Sylow定理对G进行了完全分类,证明了G共有14种同构类型:1)若P■G,则G有5种同构类型;2)若P■G,则G有9种同构类型.进而,同理构造了56阶群的13种同构类型.Let G be finite groups of order 40.Let P be Sylow 2-subroups and Q be a Sylow 5-subroup.Using the corresponding conclusions of Wang H Q's and Sylow theorem we have completely classified and showed that G consists of 14 non-isomorphic types.Here,we have provided two proofs,namely 1)If P is normal,G consists of 5 non-isomorphic types;and 2)If P is non-normal,G consists of 9 non-isomorphic types.Finally,we use the similar methods to completely classify the finite groups of order 56.

关 键 词：有限群 同构分类 生成关系 40阶 56阶 

分 类 号：O152.7[理学—数学]