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

Abstract

AbstractThe 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.