Homomorphisms into totally disconnected, locally compact groups with dense image

Title: Homomorphisms into totally disconnected, locally compact groups with dense image
Creator: Reid, Colin D.; Wesolek, Phillip R.
Relation: Forum Mathematicum Vol. 31, Issue 3, p. 685-701
Publisher Link: http://dx.doi.org/10.1515/forum-2018-0017
Publisher: Walter de Gruyter
Resource Type: journal article
Date: 2019
Description: Let ɸ : G → H be a group homomorphism such that H is a totally disconnected locally compact (t.d.l.c.) group and the image of ɸ is dense. We show that all such homomorphisms arise as completions of G with respect to uniformities of a particular kind. Moreover, H is determined up to a compact normal subgroup by the pair (G, ɸ-1 (L)), where L is a compact open subgroup of H. These results generalize the well-known properties of profinite completions to the locally compact setting.
Subject: totally disconnected locally compact groups; completions of groups; hecke pairs
Identifier: http://hdl.handle.net/1959.13/1441538
Identifier: uon:41457
Identifier: ISSN:0933-7741
Language: eng
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