Homomorphisms into totally disconnected, locally compact groups with dense image
Keyword(s):
Abstract Let {\phi:G\rightarrow 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,\phi^{-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.
1988 ◽
Vol 104
(1)
◽
pp. 47-64
2015 ◽
Vol 2015
(24)
◽
pp. 13800-13829
◽
Keyword(s):
2016 ◽
Vol 37
(7)
◽
pp. 2163-2186
◽
1988 ◽
pp. 125-140
Keyword(s):
2015 ◽
Vol 158
(3)
◽
pp. 505-530
◽
Keyword(s):