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 |
|---|---|
| Pages (from-to) | 2193-2205 |
| Number of pages | 13 |
| Journal | Communications in Algebra |
| Volume | 27 |
| Issue number | 5 |
| Publication status | Published - 1999 |
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All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
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On semi-endomorphisms of groups. / Beidar, K. I.; Fong, Y.; Ke, Wen-Fong; Wu, W. R.
In: Communications in Algebra, Vol. 27, No. 5, 1999, p. 2193-2205.Research output: Contribution to journal › Article
TY - JOUR
T1 - On semi-endomorphisms of groups
AU - Beidar, K. I.
AU - Fong, Y.
AU - Ke, Wen-Fong
AU - Wu, W. R.
PY - 1999
Y1 - 1999
N2 - 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.
AB - 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.
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M3 - Article
VL - 27
SP - 2193
EP - 2205
JO - Communications in Algebra
JF - Communications in Algebra
SN - 0092-7872
IS - 5
ER -