The number of automorphisms of a monolithic finite group

JOURNAL OF ALGEBRA

卷:322

Article

Riedl, Jeffrey M.

关键词: Finite groups;    p-Groups;    Automorphism group;    Character theory;   

DOI  :  10.1016/j.jalgebra.2009.07.034

来源: Elsevier

【 摘 要 】

We develop a general formula for the order of the group of automorphisms Aut(G) of a monolithic finite group Gin terms of information about the complex characters of G and information about how G is embedded as a subgroup of a particular finite general linear group. We show that this formula is applicable to a wide variety of finite p-groups. and we discuss several applications to particular large families of finite p-groups. Finally, we derive a useful consequence of this formula and discuss its application to a classification problem involving finite p-groups. (C) 2009 Elsevier Inc. All rights reserved

【 授权许可】

Free