Homomorphisms into totally disconnected, locally compact groups with dense image

2015/09/01 by Reid, Colin D., Wesolek, Phillip R.
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1509.00156

Abstract

Let ϕ: G → H be a group homomorphism such that H is a totally disconnected locally compact (t.d.l.c.) group and the image of ϕ 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,ϕ^-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.

Related

• The profinite completion of a group localised at a subgroup
• Totally disconnected locally compact groups with just infinite locally normal subgroups
• Expansive automorphisms of totally disconnected, locally compact groups
• Local Sylow theory of totally disconnected, locally compact groups
• A totally disconnected invitation to locally compact groups