We study topological automorphisms α of a totally disconnected,
locally compact group G which are expansive in the sense that
for some identity
neighbourhood . Notably, we prove that the automorphism induced by an expansive automorphism α on a quotient group modulo an
α-stable closed normal subgroup N is always expansive.
Further results involve the contraction groups
If α is
expansive, then is an open identity
neighbourhood in G. We give examples where fails to be a subgroup. However, is an α-stable, nilpotent open subgroup
of G if G is a closed subgroup of .
Further results are devoted to the divisible and torsion parts of ,
and to the so-called “nub”
of an expansive automorphism.