Finite Autocapable Groups with the 2-Groups of Maximal Class  

作　　者：Pengfei Bai Xiuyun Guo Jiao Wang 

机构地区：[1]School of Applied Mathematics,Shanxi University of Finance and Economics Taiyuan 030006,China [2]Department of Mathematics,Shanghai University,Shanghai 200444,China [3]Basic Courses Department,Tianjin Sino-German University of Applied Sciences Tianjin 300350,China

出　　处：《Algebra Colloquium》2024年第4期651-660,共10页代数集刊（英文版）

基　　金：National Natural Science Foundation of China(12171302,11801334);Natural Science Foundation of Shanxi Province(202103021224287);Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi(2021L278);Science&Technology Development Fund of Tianjin Education Commission for Higher Education(2019KJ141).

摘　　要：A group H is said to be autocapable if there exists a group M such that H is isomorphic to the absolute central factor group M/L(M)of M.In this paper,we first prove that if N is a characteristic subgroup of an autocapable group H,then N is neither the generalized quaternion group nor the semi-dihedral group.Next,we give the classification of finite groups G if G/L(G)is a 2-group of maximal class.

关 键 词：autocapable group absolute center 2-group of maximal class 

分 类 号：O152.1[理学—数学]