Orthomorphisms of \(Z_ p\)
type: Item
instance of: scholarly article
title: Orthomorphisms of \(Z_ p\)
zbMATH Open document ID: 0621.20006
DOI: 10.1016/0012-365X(87)90186-5
author: Anthony B. Evans
published in: Discrete Mathematics
publication date: 1987-01-01T00:00:00Z
review text: An orthomorphism of an abelian group G is a bijection \(\theta\) : \(G\to G\) for which the mapping \(\eta\) : \(G\to G\) defined by \(x\eta =x(x\theta)^{-1}\) is also a bijection. Two orthomorphisms \(\theta\) and \(\phi\) are said to be orthogonal if the mapping \(x\to x\theta (x\phi)^{-1}\) is a bijection. The orthomorphism graph of a group G has as its vertex set the orthomorphisms of G and the identity of G. Two orthomorphisms of G are adjacent in the graph if and only if they are orthogonal (every orthomorphism is adjacent to the identity mapping). Orthomorphism graphs of groups of low order have been studied by several authors. In this paper the author studies part of the orthomorphism graph of \(Z_ p\), where p is a prime number.
reviewed by: E. J. F. Primrose
Mathematics Subject Classification ID: 20D45
Mathematics Subject Classification ID: 20D60
Mathematics Subject Classification ID: 05C25
Mathematics Subject Classification ID: 20K01
Mathematics Subject Classification ID: 20K30
zbMATH DE Number: 4006513
zbMATH Keywords: abelian group
zbMATH Keywords: orthomorphisms
zbMATH Keywords: Orthomorphism graphs
MaRDI profile type: Publication
cites work: Finite Nets, I. Numerical Invariants
cites work: Generating orthomorphisms of \(GF(q)^ +\)
cites work: Q3695922
cites work: Complete mappings of finite groups
cites work: Orthomorphisms of Groups and Orthogonal Latin Squares. I
cites work: The Construction of Orthogonal Latin Squares
cites work: On orthogonal Latin squares
cites work: Q3700375
cites work: Neofields
cites work: A Class of Groups Associated with Latin Squares
cites work: Q5538955
cites work: Q5682970
description: scientific article; zbMATH DE number 4006513