Coleman Automorphisms of Generalized Dihedral Groups

作     者：Zheng Xing LI Yuan Lin LI 

作者机构：Colledge of AutomationEngineeringQingdao University Department of MathematicsBrock University 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2016年第32卷第2期

页      面：251-257页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Supported by a Discovery Grant from the Natural Science and Engineering Research Council of Canada the National Natural Science Foundation of China(Grant Nos.71171120,71571108,11401329) the Project of International(Regional) Cooperation and Exchanges of NSFC(Grant No.71411130215) the Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.20133706110002) the Natural Science Foundation of Shandong Province(Grant No.ZR2015GZ007) the Doctoral Fund of Shandong Province(Grant No.BS2012SF003) the Project of Shandong Province Higher Educational Science and Technology Program(Grant No.J14LI10) the Project of Shandong Province Higher Educational Excellent Backbone Teachers for International Cooperation and Training 

主　　题：Coleman automorphism generalized dihedral group 

摘      要：Let D be a generalized dihedral group and Autcol（D） its Coleman automorphism group. Denote by Outcol（D） the quotient group of Autcol（D） by Inn（D）, where Inn（D） is the inner automorphism group of D. It is proved that either Outcol（D） = i or Outcol（D） is an elementary abelian 2-group whose order is completely determined by the cardinality of π（D）. Furthermore, a necessary and sufficient condition for Outcol（D） = 1 is obtained. In addition, whenever Outcol（D） ≠ 1, it is proved that Autcol（D） is a split extension of Inn（D） by an elementary abelian 2-group for which an explicit description is given.