The Scale and Tidy Subgroups for Endomorphisms of Totally Disconnected Locally Compact Groups

Abstract

The scale of an endomorphism, $\alpha$, of a totally disconnected, locally compact group $G$ is the minimum index $[\alpha (U):\alpha (U)\cap U]$, 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 $\alpha$ from previously understood case when $\alpha$ is an automorphism to the case when $\alpha$ is merely an endomorphism.

arXiv comment34 pages

References in corpus (1)

• Tidy subgroups for commuting automorphisms of totally disconnected groups: an analogue of simultaneous triangularisation of matrices