## Abstract

Given a group G, a mapping α : G → G is said to be a semi-endomorphism of G if α(x + y + x) = α(x) + α(y) + α(x) 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(S_{n}) of S_{n}, with n ≥ 3 is equal to E(S_{n}) + M_{c}(S_{n}), where E(S_{n}) is the endomorphism nearring of S_{n}, and M_{C}(S_{n}) is the nearring of constant mappings of S_{n}.

Original language | English |
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Pages (from-to) | 2193-2205 |

Number of pages | 13 |

Journal | Communications in Algebra |

Volume | 27 |

Issue number | 5 |

Publication status | Published - 1999 Dec 1 |

## All Science Journal Classification (ASJC) codes

- Algebra and Number Theory