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Endomorphism near-rings of $ p$-groups generated by the automorphism and inner automorphism groups


Author: Gary L. Peterson
Journal: Proc. Amer. Math. Soc. 119 (1993), 1045-1047
MSC: Primary 16Y30; Secondary 20D45, 20F28
MathSciNet review: 1162092
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Abstract: The purpose of this paper is to investigate the equality of the endomorphism near-rings generated by the automorphism group and inner automorphism group of a nonabelian $ p$-group $ G$. If the automorphism group of $ G$ is not a $ p$-group, we find that these near-rings are different. If the automorphism group of $ G$ is a $ p$-group, examples are given illustrating that these near-rings can be different and can be the same.


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] D. Gorenstein, Finite groups, Harper and Row, New York, 1968. MR 0231903 (38:229)
  • [3] B. Huppert, Endliche Gruppen. I, Springer-Verlag, Berlin, 1967. MR 0224703 (37:302)
  • [4] C. Lyons and G. Peterson, Local endomorphism near-rings, Proc. Edinburgh Math. Soc. 31 (1988), 409-414. MR 969070 (89m:16077)
  • [5] J. Malone and C. Lyons, Finite dihedral groups and d.g. near-rings. II, Compositio Math. 26 (1973), 249-259. MR 0330236 (48:8574)
  • [6] J. Meldrum, Near-rings and their links with groups, Pitman, London, 1985. MR 854275 (88a:16068)
  • [7] G. Peterson, Automorphism groups emitting local endomorphism near-rings, Proc. Amer. Math. Soc. 105 (1989), 840-843. MR 952320 (89k:20051)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1162092-0
Keywords: Endomorphism near-ring, automorphism group, inner automorphism group
Article copyright: © Copyright 1993 American Mathematical Society