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

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

Abstract

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 ).

Keywords

Proper Subset Homomorphic Image Orbit Type Property Versus Stabilizer Subgroup 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  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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