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一类圈积的自同构群的矩阵描述 被引量:1

A Matrix Description of Automorphism Groups for Certain Wreath Products
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摘要 使用Bidwell和Curran在2006年引入的描述半直积的自同构的矩阵方法,结合作者等人在2010年证明的关于稳定自同构群的矩阵公式,得到了一类正则圈积的自同构群的矩阵描述,并求出了自同构群的阶. It is obtained a matrix description of automorphism groups and its order for certain regular wreath products, by using the matrix method to characterize automorphisms of semi-direct products introduced by Bidwell and Curran in 2006, combined with a matrix formula for stable automorphism groups presented by the authors in 2010.
作者 周芳
出处 《数学的实践与认识》 CSCD 北大核心 2013年第14期284-288,共5页 Mathematics in Practice and Theory
基金 山西省自然科学基金(2013011001-3)
关键词 圈积 自同构 半直积 矩阵 wreath product automorphism semi-direct product matrix
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参考文献4

  • 1Bidwell J N S, Curran M J. The automorphism group of a split metacyclic p-group[J]. Arch Math, 2006, 87: 488-497.
  • 2Zhou F, Liu H G. Automorphism groups of semidirect products[J]. Arch Math, 2008, 91: 193-198.
  • 3周芳,马玉杰,刘合国.半直积的稳定自同构群[J].数学进展,2010,39(6):673-678. 被引量:5
  • 4Isaacs I M. Finite Group Theory[M]. American Mathematical Society, 2008.

二级参考文献3

  • 1Robinson, D.J.S., A Course in the Theory of Groups (Second Edition), Springer-Verlag, New York-Heidelberg- Berlin, 1996.
  • 2Bidwell, J.N.S, Curran, M.J., The automorphism group of a split metacyclic p-group, Arch. Math., 2006, 87: 488-497.
  • 3樊恽,黄平安.分裂扩张的稳定自同构群[J].数学年刊(A辑),2001,22(6):791-796. 被引量:9

共引文献4

同被引文献7

  • 1ISAACS I M. Finite group theory [M]. Providence, Rhode Island, America: American Mathematical So- ciey, 2008.
  • 2BIDWELL J N S, CURRAN M J. The automorphism group of a split metacyclic p-group [J]. Archiv Der Mathematic, 2006, 87(6): 488-497.
  • 3ZHOU F, LIU H G. Automorphism groups of semidi- reet products[J]. Archiv Der Mathematic, 2008, 91 (3) : 193-198.
  • 4HUPPERT B. Endliche gruppen I. [M]. Berlin.. Springer-Verlag, 1967.
  • 5FOULADI S, ORFI R. The automorphism group of a finite minimal non-abelian p-group [J]. Math Reports, 2014, 16(66).. 133-139.
  • 6ROBINSON D J S. A Course in the theory of groups [M]. New York: Springer-Verlag, 1982.
  • 7周芳,马玉杰,刘合国.半直积的稳定自同构群[J].数学进展,2010,39(6):673-678. 被引量:5

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