We describe finite-dimensional smooth Lie groups over local fields of positive characteristic which do not admit an analytic Lie group structure compatible with the given topological group structure, and C^n-Lie groups without a compatible C^{ n+1}-Lie group structure, for each positive integer n. We also present examples of non-analytic, smooth automorphisms of Lie groups over such fields, as well as C^n-automorphisms which fail to be C^{ n+1}.
Categories: math.GR