Elementary proofs that \(Z_p^2\) and \(Z_p^3\) are CI-groups
type: Item
instance of: scholarly article
title: Elementary proofs that \(Z_p^2\) and \(Z_p^3\) are CI-groups
zbMATH Open document ID: 0942.05031
author: Lewis A. Nowitz
author: Brian Alspach
published in: European Journal of Combinatorics
publication date: 2000-08-15T00:00:00Z
review text: A Cayley graphical object on a group \(G\) is either a Cayley graph, Cayley digraph, or Cayley color digraph. \(G\) is said to be a CI group if every isomorphism between two Cayley graphical objects on \(G\) may be derived from a group automorphism. \textit{C. D. Godsil} [Ars Comb. 15, 231-246 (1983; Zbl 0519.05036)] proved using deep results about primitive groups that \(Z_p^2\) is a CI group on the class of Cayley graphs. In this paper it is shown, using only facts about Sylow \(p\) subgroups and the structure of the graphs involved that \(Z_p^2\) and \(Z_p^3\) are CI groups.
reviewed by: Brigitte Servatius
Mathematics Subject Classification ID: 05C25
Mathematics Subject Classification ID: 05C20
Mathematics Subject Classification ID: 05C60
zbMATH DE Number: 1382653
zbMATH Keywords: Cayley graph
zbMATH Keywords: Cayley isomorphism property
MaRDI profile type: Publication
full work available at URL: eujc.1999.0309
OpenAlex ID: W1975267010
cites work: Isomorphism problem for a class of point-symmetric structures
cites work: On isomorphisms of finite Cayley graphs
cites work: Isomorphism problem for Cayley graphs of \(\mathbb{Z}^ 3_ p\)
cites work: Q3669446
cites work: On the isomorphism problem for finite Cayley graphs of bounded valency
cites work: Isomorphisms of finite Cayley digraphs of bounded valency
cites work: A non-Cayley-invariant Cayley graph of the elementary Abelian group of order 64
DOI: 10.1006/EUJC.1999.0309
description: scientific article; zbMATH DE number 1382653