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Distributively generated centralizer near-rings

Authors: C. J. Maxson and K. C. Smith
Journal: Proc. Amer. Math. Soc. 87 (1983), 409-414
MSC: Primary 16A76
MathSciNet review: 684628
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Abstract: Let $ G$ be a finite group. $ \mathcal{A}$ a group of automorphisms of $ G$ and $ \mathcal{C}\left( {\mathcal{A};G} \right)$ the centralizer near-ring determined by the pair $ (\mathcal{A},G)$. In this paper we investigate the structure of those centralizer near-rings $ \mathcal{C}\left( {\mathcal{A};G} \right)$ which are distributively generated. Particular attention is given to the situation in which $ G$ is a solvable group.

References [Enhancements On Off] (What's this?)

  • [1] A Fröhlich, The near-ring generated by the inner automorphisms of a finite simple group, J. London Math. Soc. 33 (1958), 95-107. MR 0093543 (20:67)
  • [2] R. R. Laxton, Primitive distributively generated near-rings, Mathematika 8 (1961), 143-158. MR 0141688 (25:5085)
  • [3] C. J. Maxson and K. C. Smith, The centralizer of a set of group automorphisms, Comm. Algebra 8 (1980), 211-230. MR 558111 (81c:16048)
  • [4] C. J. Maxson, M. R. Pettet and K. C. Smith, On semisimple rings that are centralizer near-rings, Pacific J. Math. (to appear). MR 675410 (83m:16036)
  • [5] G. Pilz, Near-rings, North-Holland, New York, 1977. MR 0469981 (57:9761)
  • [6] J. J. Rotman, The theory of groups, an introduction, 2nd ed., Allyn & Bacon, Boston, Mass., 1973. MR 0442063 (56:451)

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Keywords: Centralizer-near rings, distributively generated near-rings
Article copyright: © Copyright 1983 American Mathematical Society

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