Acta mathematica scientia,Series A ›› 2012, Vol. 32 ›› Issue (2): 344-348.

• Articles • Previous Articles     Next Articles

Coleman Automorphisms of Semidirect Products of Abelian Groups by p-groups of Maximal Class

 LI Zheng-Xing, HAI Jin-Ke   

  1. College of Mathematics, Qingdao University, Shandong Qingdao 266071
  • Received:2010-07-08 Revised:2011-12-06 Online:2012-04-25 Published:2012-04-25
  • Supported by:

    国家自然科学基金(11071155, 11171169)和山东省自然科学基金(Y2008A03)资助

Abstract:

Let G=A×P be the  semidirect product of an abelian group A and a p-group P of maximal class, where P acts on A by leaving every cyclic subgroup of A invariant. It is shown that every Coleman automorphism of G is an inner automorphism. As an immediate consequence, we obtain that the normalizer property holds for such group G.

Key words: Integral group ring, Coleman automorphism, Normalizer property

CLC Number: 

  • 20C05
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