Let G be a group. A weak Cayley table isomorphism $\phi$: G $\rightarrow$ G is a bijection satisfying two conditions: (i) $phi$ sends conjugacy classes to conjugacy classes; and (ii) $\phi$(g1)$\phi$(g2) is conjugate to $\phi$(g1g2) for all g1, g2 in G. The set of all such mappings forms a group W(G) under composition. We study W(G) for fifty-six of the two hundred nineteen three-dimensional crystallographic groups G as well as some other groups. These fifty-six groups are related to our previous work on wallpaper groups.
College and Department
Physical and Mathematical Sciences; Mathematics
BYU ScholarsArchive Citation
Paulsen, Rebeca Ann, "Weak Cayley Table Groups of Crystallographic Groups" (2021). Theses and Dissertations. 9339.
crystallographic groups, automorphisms, weak Cayley table isomorphisms