一类有限群构造的新证明

一类有限群构造的新证明 A Simply Proof for the Structures of A Kind of NonAbelian Groups 黄本文 HUANG BenWen 1 first-author 武汉大学数学科学学院,湖北,武汉,430072 武汉大学数学科学学院,湖北,武汉,430072 School of Mathematical Science,Wuhan University School of Mathematical Science,Wuhan University 利用Fitting子群的特性及子群的扩张原理 ,证明了一类非交换群的构造即 2 3P（P =3,7）阶群的构造 :① 2 3·7阶群共有 13型 ;② 2 3·3阶群共有 15型 .这是一种最新的证明方法 ,该方法思路简明 ,证明篇幅较短 . By the characters of Fitting subgroup and extending theorems of subgroup ,the author shows the structure of a kind of nonAbelian groups.That is the structure of a group with order 2 3 p（p=3 or 7）.The author proves that the proup with order 2 3 7 has 13 types and the group with order 2 3 3 has 15 types .The proving method has not been found before and it is very precise.It opens a new road for researching the structure of finite groups. 扩张 可解群 自同构群 Fitting子群 extension solvable groups automorphism group Fitting subgroup O152.1 湖北省自然科学基金!资助项目 （99J1 65） 2001-01-01 2021-04-01 1