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 Sn, 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(Sn) is the nearring of constant mappings of Sn.
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