On semi-endomorphisms of groups

K. I. Beidar, Y. Fong, W. F. Ke, W. R. Wu

Research output: Contribution to journalArticlepeer-review

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 Dec 1

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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