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  • Author: C. R. E. Raja x
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Abstract

We study topological automorphisms α of a totally disconnected, locally compact group G which are expansive in the sense that

nαn(U)={1}

for some identity neighbourhood UG. Notably, we prove that the automorphism induced by an expansive automorphism α on a quotient group G/N modulo an α-stable closed normal subgroup N is always expansive. Further results involve the contraction groups

Uα:={gG:αn(g)1 as n}.

If α is expansive, then UαUα-1 is an open identity neighbourhood in G. We give examples where UαUα-1 fails to be a subgroup. However, UαUα-1 is an α-stable, nilpotent open subgroup of G if G is a closed subgroup of GLn(p). Further results are devoted to the divisible and torsion parts of Uα, and to the so-called “nub” nub(α)=Uα¯Uα-1¯ of an expansive automorphism.