Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-27T10:32:46.769Z Has data issue: false hasContentIssue false
  • English
  • Français

Near-rings of mappings on finite topological groups

Part of: Topological and differentiable algebraic systems

Published online by Cambridge University Press:  09 April 2009

Gordon Mason
Gordon Mason
Affiliation:
Department of Mathematics & Statistics University of New Brunswick Fredericton, N. B., Canada
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

When G is a topological group, the set N(G) of continuous self-maps of G, and the subset N0(G) of those which fix the identity of G, are near-rings. In this paper we examine the (left) ideal structure of these near-rings when G is finite. N0(G) is shown to have exactly two maximal ideals, whose intersection is the radical. In the final section we investigate subnear-rings of N0(G) determined by certain continuous elements of the endomorphism near-ring.

MSC classification

Secondary: 22A99: None of the above, but in this section
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 38 , Issue 1 , February 1985 , pp. 92 - 102
Copyright
Copyright © Australian Mathematical Society 1985

References

[1]Fong, Y. and Meldrum, J. D. P., ‘The endomorphism near-rings of the symmetric groups of degree at least five’, J. Austral. Math. Soc. Ser. A 30 (1980), 37–49.CrossRefGoogle Scholar
[2]Higgins, P. J., An introduction to topological groups (Cambridge University Press, 1974).Google Scholar
[3]Hofer, R. D., ‘Near-rings of continuous functions on disconnected groups’, J. Austral Math. Soc. Ser. A 28 (1979), 433–451.CrossRefGoogle Scholar
[4]Johnson, M., ‘Radicals of endomorphism near-rings’, Rocky Mountain J. Math. 3 (1973), 1–7.CrossRefGoogle Scholar
[5]Malone, J. J., ‘Generalized quaternion groups and distributively generated near-rings’, Proc. Edinburgh Math. Soc. 18 (1973), 235–238.CrossRefGoogle Scholar
[6]Malone, J. J. and Lyons, C., ‘Finite dihedral groups and d. g. near-rings I’, Compositio Math. 24 (1972), 305–312.Google Scholar
[7]Malone, J. J. and Lyons, C., ‘Finite dihedral groups and d. g. near-rings II’, Compositio Math. 26 (1973), 249–259.Google Scholar
[8]Pilz, G., Near-rings (North-Holland, Amsterdam, 1977).Google Scholar
[9]Schenkman, E., Group theory (Van Nostrand, Princeton, N. J., 1965).Google Scholar