Abstract
Let S be a finite generating set of a torsion-free, nilpotent group G. We show that every automorphism of the Cayley graph Cay(G; S) is affine. (That is, every automorphism of the graph is obtained by composing a group automorphism with multiplication by an element of the group.) More generally, we show that if Cay(G(1); S-1) and Cay(G(2); S-2) are connected Cayley graphs of finite valency on two nilpotent groups G(1) and G(2), then every isomorphism from Cay(G(1); S-1) to Cay(G(2); S-2) factors through to a well-defined affine map from G(1)/N-1 to G(2)/N-2, where is the torsion subgroup of G,. For the special case where the groups are abelian, these results were previously proved by A. A. Ryabchenko and C. Loh, respectively.
Original language | English |
---|---|
Pages (from-to) | 453-467 |
Number of pages | 15 |
Journal | NEW YORK JOURNAL OF MATHEMATICS |
Volume | 22 |
Publication status | Published - 4 Jun 2016 |