We analyze the structure of locally compact groups which can be built up from p-adic Lie groups, for p in a given set of primes. In particular, we calculate the scale function and determine tidy subgroups for such groups, and use them to recover the primes needed to build up the group.
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.