Weak Cayley table groups of some crystallographic groups

Stephen P. Humphries; Rebeca A. Paulsen

paper

Weak Cayley table groups of some crystallographic groups

arXiv:1603.03702

Abstract

For a group $G$ , a weak Cayley isomorphism is a bijection $f : G \to G$ such that $f (g_{1} g_{2})$ is conjugate to $f (g_{1}) f (g_{2})$ for all $g_{1}, g_{2} \in G$ . They form a group $W (G)$ that is the group of symmetries of the weak Cayley table of $G$ . We determine $W (G)$ for each of the seventeen wallpaper groups $G$ , and for some other crystallographic groups.