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Centralizer Near-Rings Determined by End g

Chapter
Part of the Mathematics and Its Applications book series (MAIA, volume 336)

Abstract

Let G be a group. The structure of the centralizer near-ring M E (G) = {f: GG | fσ = σf for every σ ∈ End G} is investigated for the cases in which G is a finitely generated abelian, characteristically simple, symmetric or generalized quaternion group.

Keywords

Abelian Group Normal Subgroup Conjugacy Class Simple Group Pairwise Disjoint 
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.
    G. A. Cannon, Centralizer Near-Rings Determined by End G, Doctoral Dissertation, Texas A&M University, to appear.Google Scholar
  2. 2.
    J. R. Clay, Nearrings: Geneses and Applications, Oxford Science Publ., Oxford, 1992.zbMATHGoogle Scholar
  3. 3.
    Y. Fong and J. D. P. Meldrum, Endomorphism Near-Rings of a Direct Sum of Isomorphic Finite Simple Nonabelian Groups, Near-Rings and Near-Fields ed. G. Betsch, North-Holland, Amsterdam, 1987, 73–78.Google Scholar
  4. 4.
    D. Gorenstein, Finite Groups, Harper & Row, New York, 1968.zbMATHGoogle Scholar
  5. 5.
    J. J. Malone, Generalized Quaternion Groups and Distributively Generated Near-Rings, Proc. Edinburgh Math. Soc., 18 (1973), 235–238.MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    C. J. Maxson, M. R. Pettet and K. C. Smith, On Semisimple Rings that are Centralizer Near-Rings, Pacific J. Math., 101 (1981), 451–461.MathSciNetCrossRefGoogle Scholar
  7. 7.
    C. J. Maxson and K. C. Smith, The Centralizer of a Set of Group Automorphisms, Comm. Alg., 8 (1980), 211–230.MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    C. J. Maxson and K. C. Smith, Centralizer Near-Rings Determined by Local Rings, Houston J. Math., 11 (1985), 355–366.MathSciNetzbMATHGoogle Scholar
  9. 9.
    G. Pilz, Near-Rings, North Holland/American Elsevier, Amsterdam, second, revised edition, 1983.zbMATHGoogle Scholar
  10. 10.
    W. R. Scott, Group Theory, Dover, New York, 1987.zbMATHGoogle Scholar
  11. 11.
    M. Suzuki, Group Theory I, Springer-Verlag, 1982.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1995

Authors and Affiliations

  1. 1.Department of MathematicsTexas A&M UniversityCollege StationUSA

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