Orthomorphisms of \(Z_ p\)
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.
scientific article; zbMATH DE number 4006513
scientific article