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 autocap...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.展开更多
基金National Natural Science Foundation of China(12171302,11801334)Natural Science Foundation of Shanxi Province(202103021224287)+1 种基金Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi(2021L278)Science&Technology Development Fund of Tianjin Education Commission for Higher Education(2019KJ141).
文摘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.
