We construct Graev ultrametrics on free products of groups with two-sided invariant ultrametrics and HNN extensions of such groups. We also introduce a notion of a free product of general Polish groups and prove, in particular, that two Polish groups G and H can be embedded into a Polish group T in such a way that the subgroup of T generated by G and H is isomorphic to the free product G * H.
Funding source: Denmark's Council for Independent Research (Natural Sciences Division)
Award Identifier / Grant number: 10-082689/FNU
Funding statement: Research supported by Denmark's Council for Independent Research (Natural Sciences Division), Grant No. 10-082689/FNU.
The author wants to thank the anonymous referee for helping to improve the exposition.
© 2016 by De Gruyter