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 ).


Proper Subset Homomorphic Image Orbit Type Property Versus Stabilizer Subgroup 
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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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