A Two Dimensional Version of the Goldschmidt-Sims Conjecture.

Abstract.

The Goldschmidt-Sims conjecture asserts that there is a finite number of (conjugacy classes of)
edge transitive lattices in the automorphism group of a regular tree with prime valence.
We prove a similar theorem for irreducible lattices, transitive on the 2-cells of the product of two regular trees of prime valences.