On semi-endomorphisms of groups

K. I. Beidar, Y. Fong, Wen-Fong Ke, W. R. Wu

Research output: Contribution to journalArticle

2 Citations (Scopus)

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 languageEnglish
Pages (from-to)2193-2205
Number of pages13
JournalCommunications in Algebra
Volume27
Issue number5
Publication statusPublished - 1999

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Endomorphism
Endomorphisms
Near-ring
Automorphism
Finite Simple Group
Symmetric group
Zero

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Cite this

Beidar, K. I., Fong, Y., Ke, W-F., & Wu, W. R. (1999). On semi-endomorphisms of groups. Communications in Algebra, 27(5), 2193-2205.
Beidar, K. I. ; Fong, Y. ; Ke, Wen-Fong ; Wu, W. R. / On semi-endomorphisms of groups. In: Communications in Algebra. 1999 ; Vol. 27, No. 5. pp. 2193-2205.
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Beidar, KI, Fong, Y, Ke, W-F & Wu, WR 1999, 'On semi-endomorphisms of groups', Communications in Algebra, vol. 27, no. 5, pp. 2193-2205.

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 journalArticle

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Beidar KI, Fong Y, Ke W-F, Wu WR. On semi-endomorphisms of groups. Communications in Algebra. 1999;27(5):2193-2205.