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.
|Number of pages||13|
|Journal||Communications in Algebra|
|Publication status||Published - 1999 Dec 1|
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory