2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66549Let αbe an automorphism of the totally disconnected group G. The compact open subgroup, V, if G is tidy for αif [α(V') : α(V')\cap V'] is minimised at V, where V' ranges over all compact open subgroups of G. Identifying a subgroup tidy for αis analogous to identifying a basis which puts a linear transformation into Jordan canonical form. This analogy is developed here by showing that commuting automorphisms have a common tidy subgroup of G and, conversely, that a group H of automorphisms having a common tidy subgroup V is abelian modulo the automorphisms which leave V invariant. Certain subgroups of G are the analogues of eigenspaces and corresponding real characters of H the analogues of eigenvalues.36 pages, submitted keywords: locally compact group, scale function, tidy subgroup, modular function, automorphismGroup Theory22D05 (Primary); 22D45, 20E25, 20E36 (Secondary)text