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Coleman Automorphisms of Generalized Dihedral Groups

Zheng Xing LI  Yuan Lin LI  
【摘要】:Let D be a generalized dihedral group and Aut_(Col)(D) its Coleman automorphism group.Denote by Out_(Col)(D) the quotient group of Aut_(Col)(D) by Inn(D),where Inn(D) is the inner automorphism group of D.It is proved that either Out_(Col)(D) = 1 or Out_(Col)(D) is an elementary abelian2-group whose order is completely determined by the cardinality of π(D).Furthermore,a necessary and sufficient condition for Out_(Col)(D) = 1 is obtained.In addition,whenever Out_(Col)(D) ≠ 1,it is proved that Aut_(Col)(D) is a split extension of Inn(D) by an elementary abelian 2-group for which an explicit description is given.

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