Locally compact groups built up from p-adic Lie groups, for p in a given set of primes

Abstract

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.

25 pages, LaTeX; v2: A counterexample has been added which shows that (as desired) the two construction principles yield different classes of groups