A. J. Sutherland

Preprint Sep 2026

Finite-valued invariant metrics and a classification of natural groups

For every group $G$, of arbitrary cardinality, we construct a right-invariant metric with at most $32$ values whose isometries are exactly the permutations preserving every right-invariant metric on $G$. The proof combines subgroup-entry ranks and sign-variation colorings with a short-word rigidity theorem of Leemann a...

A. J. Sutherland · 1 citation

Preprint Oct 2026

Watkins's conjecture holds for all infinite groups

We prove that at every infinite cardinality, every group which is neither abelian of exponent greater than two nor generalized dicyclic admits a graphical regular representation, settling the infinite-group part of Watkins's conjecture. We also determine the Cayley index of every infinite group: it is $1$, $2$, or $8$,...

A. J. Sutherland · 0 citations

Preprint Sep 2026

Finite-valued invariant metrics and a classification of natural groups

For every group $G$, of arbitrary cardinality, we construct a right-invariant metric with at most $32$ values whose isometries are exactly the permutations preserving every right-invariant metric on $G$. The proof combines subgroup-entry ranks and sign-variation colorings with a short-word rigidity theorem of Leemann a...

A. J. Sutherland · 0 citations