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Licensed Unlicensed Requires Authentication Published by De Gruyter January 29, 2015

Graev ultrametrics and free products of Polish groups

Konstantin Slutsky
From the journal Forum Mathematicum

Abstract

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.

MSC: 03E15; 54H05

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.

Received: 2014-2-24
Revised: 2014-9-11
Published Online: 2015-1-29
Published in Print: 2016-5-1

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