Hostname: page-component-745bb68f8f-grxwn Total loading time: 0 Render date: 2025-02-05T16:59:46.806Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Fuchs, P.. Isomorphisms between lattices of filters and lattices of substructures in transformations near-rings (Submitted).Google Scholar
2Jacobson, N.. Lectures in Abstract Algebra II (New York: Van Nostrand, 1953).CrossRefGoogle Scholar
3Jech, T.. Set Theory (New York: Academic Press, 1978).Google Scholar
4Maxson, C. J. and Smith, K. C.. The centralizer of a set of group automorphisms. Comm. Algebra 8 (1980), 211–230.CrossRefGoogle Scholar
5Meldrum, J. D. P. and Zeller, M.. The simplicity of near-rings of mappings. Proc. Roy. Soc. Edinburgh Sec. A 90 (1981), 185–193.CrossRefGoogle Scholar
6Pilz, G.. Near-rings, revised edn. (Amsterdam: North-Holland, 1983).Google Scholar