Elementary proofs that \(Z_p^2\) and \(Z_p^3\) are CI-groups
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.
scientific article; zbMATH DE number 1382653