When is a centralizer near-ring isomorphic to a matrix near-ring? Part 2

  • Alan Oswald
  • Kirby C. Smith
  • Leon van Wyk


Let G be a finite group and A a group of automorphisms of G. It is always the case that for every integer n ≥ 2 the matrix near-ring \( \mathbb{M}_n \)(M A (G);G) is a subnear-ring of the centralizer near-ring M A (G n ). We find conditions such that \( \mathbb{M}_n \)(M A (G);G) is a proper subset of M A (G n ). Assuming both A and G are abelian we find conditions under which \( \mathbb{M}_n \)(M A (G);G) equals M A (G n ).


Cond Alan 


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  1. [1]
    C. J. Maxson and K. C. Smith, The centralizer of a set of group automorphisms, Comm. Alg. 8 (1980), 211–230.MathSciNetMATHCrossRefGoogle Scholar
  2. [2]
    J. D. P. Meldrum and A. P. J. van der Walt, Matrix near-rings, Arch. Math. 47 (1986), 312–319.MATHCrossRefGoogle Scholar
  3. [3]
    I. Niven, H. Zuckerman and H. Montgomery, An introduction to the theory of numbers. John Wiley & Sons, New York (1991).Google Scholar
  4. [4]
    G. Pilz, Near-rings (second edition), North Holland/American Elsevier, Amsterdam (1983).Google Scholar
  5. [5]
    K.C. Smith, Generalized matrix near-rings, Comm. Alg. 24 (1996), 2065–2077.MATHCrossRefGoogle Scholar
  6. [6]
    K.C. Smith, Rings which are a homomorphic image of a centralizer near-ring, in Proc. of the 1993 Fredericton Conference on near-rings and near-fields, (eds. Y. Fong et al). Kluwer Academic Publishers (1995), 257–270.Google Scholar
  7. [7]
    K.C. Smith and L. van Wyk, When is a centralizer near-ring isomorphic to a matrix near-ring? Comm. Alg. 24 (1996), 4549–4562.MATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2001

Authors and Affiliations

  • Alan Oswald
    • 1
  • Kirby C. Smith
    • 2
  • Leon van Wyk
    • 3
  1. 1.School of Computing and MathematicsUniversity of TeessideMiddlesbrough, ClevelandEngland
  2. 2.Department of MathematicsTexas A & M UniversityCollege StationUSA
  3. 3.Department of MathematicsUniversity of StellenboschMatielandSouth Africa

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