Abstract
Given a group G, a mapping αG→G is said to be a semi-endomorphism of G if for all x,y ∈ G. It is shown that any non-trivial zero preserving semi-endomorphism of a finite simple group of order greater than two is either an automorphism or an anti-automorphism. Moreover, the semi-endomorphisms of S n, the symmetric group of degree n n ≥ 4, are described. As an application, it is proved that the semi-endomorphism nearring S(Sn ) of Sn with n ≥ 3 is equal to E(Sn ) + Mc (Sn ) where E(Sn )is the endomorphism nearring of Sn , and Mc (S n) is the nearring of constant mappings of Sn .
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