Commensurators of solvable S-arithmetic groups

Abstract

We show that the abstract commensurator of an S-arithmetic subgroup of a solvable algebraic group over Q is isomorphic to the Q-points of an algebraic group, and compare this with examples of nonlinear abstract commensurators of S-arithmetic groups in positive characteristic. In particular, we include a description of the abstract commensurator of the lamplighter group.

15 pages

References in corpus (1)

• Automorphism groups of polycyclic-by-finite groups and arithmetic groups