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.