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The scale of an endomorphism, α, of a totally disconnected, locally compact group G is the minimum index [α(U):α(U)∩U], for U a compact, open subgroup of G. A structural characterization of subgroups at which the minimum is attained is established. This characterization extends the notion of subgroup tidy for α from the previously understood case when α is an automorphism to the case when α is merely an endomorphism

The scale and tidy subgroups for endomorphisms of totally disconnected locally compact groups