  We define a local Sylow subgroup of a totally disconnected, locally compact
group G to be a maximal pro-p subgroup of an open compact subgroup of G. We use
these subgroups to define the p-localisation of G, a locally virtually pro-p
group which maps continuously and injectively to G with dense image, and
describe the relationship between the scale and modular functions of G and
those of its p-localisation. In the case of locally virtually prosoluble
groups, we consider all primes simultaneously using local Sylow bases.
