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 pro...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.展开更多
基金Supported by a Discovery Grant from the Natural Science and Engineering Research Council of Canadathe National Natural Science Foundation of China(Grant Nos.71171120,71571108,11401329)+5 种基金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
文摘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.
