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The endomorphism near-rings of the symmetric groups of degree at least five

Published online by Cambridge University Press:  09 April 2009

Y. Fong  and
J. D. P. Meldrum
Y. Fong
Affiliation:
Department of Mathematics King's Buildings, Mayfield Road Edinburgh EH9 3JZ, U.K.
J. D. P. Meldrum
Affiliation:
Department of Mathematics King's Buildings, Mayfield Road Edinburgh EH9 3JZ, U.K.
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Abstract

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The near-ring distributively generated by the semigroup of all endomorphisms of Sn, the symmetric group of degree n, for n ≥ 5, is close to being the near-ring of all mappings from Sn to itself respecting the identity. In this paper, the structure of these near-rings is studied in detail. In particular, addition and multiplication rules for the elements given in canonical form are determined. A complete list of all right ideals, left ideals, right invariant and left invariant subgroups is given.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 30 , Issue 1 , September 1980 , pp. 37 - 49
Copyright
Copyright © Australian Mathematical Society 1980

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