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Centraliser near-rings determined by fixed point free automorphism groups

Published online by Cambridge University Press:  14 November 2011

Peter Fuchs ,
C. J. Maxson ,
M. R. Pettet  and
K. C. Smith
Peter Fuchs
Affiliation:
Department of Mathematics, Texas A&M University, College Station, Texas 77843, U.S.A.
C. J. Maxson
Affiliation:
Department of Mathematics, Texas A&M University, College Station, Texas 77843, U.S.A.
M. R. Pettet
Affiliation:
Department of Mathematics, University of Toledo, Toledo, Ohio 43606, U.S.A.
K. C. Smith
Affiliation:
Department of Mathematics, Texas A&M University, College Station, Texas 77843, U.S.A.
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Synopsis

Let G be a group and let A be a fixed point free group of automorphisms of G. It is shown that the centraliser near-ring MA(G) has at most one nontrivial ideal. Conditions on the pair (A, G) are given which force MA(G) to be simple. It is shown that if a nonsimple near-ring MA(G) exists, then A and G have unusual properties.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 107 , Issue 3-4 , 1987 , pp. 327 - 337
Copyright
Copyright © Royal Society of Edinburgh 1987

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References

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