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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826 (e) ISSN 0002-9939 (p)
     

On an Isomorphism Problem for Endomorphism Near-Rings

Author(s): Gary L. Peterson
Journal: Proc. Amer. Math. Soc. 126 (1998), 1897-1900.
MSC (1991): Primary 16Y30; Secondary 20E36
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Abstract | References | Similar articles | Additional information

Abstract: Suppose $R$ and $S$ are endomorphism near-rings generated by
groups of automorphisms containing the inner automorphisms of two respective finite perfect groups $G$ and $H$. In this note we show that if $R$ and $S$ are isomorphic, then $G/Z(G)$ and $H/Z(H)$ are isomorphic.


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C. G. Lyons and J. D. P. Meldrum, $N$-series and tame near-rings, Proc. Royal Soc. Edinburgh, 86A(1980), 153-163. MR 82d:16033
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J. D. P. Meldrum, Near-Rings and their links with groups, Pitman, London, 1985. MR 88a:16068
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G. L. Peterson, On the structure of an endomorphism near-ring, Proc. Edinburgh Math. Soc., 32(1989), 223-229. MR 90e:16063
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S. A. Syskin, On a problem of C. Lyons and G. Mason, to appear
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S. D. Scott, Tame near-rings and $N$-groups, Proc. Edinburgh Math. Soc., 23(1980), 275-296. MR 83b:16032
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Additional Information:

Gary L. Peterson
Affiliation: Department of Mathematics James Madison University Harrisonburg, Virginia 22807
Email: peterson@math.jmu.edu

DOI: 10.1090/S0002-9939-98-04302-0
PII: S 0002-9939(98)04302-0
Keywords: Near-ring, endomorphism near-ring
Received by editor(s): June 30, 1996
Received by editor(s) in revised form: December 6, 1996
Communicated by: Lance W. Small
Copyright of article: Copyright 1998, American Mathematical Society


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