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Tue, 16 Jun 2026

14:00 - 15:00
L6

The question of profinite isomorphism

Dan Segal
(Oxford)
Abstract

The question is this:  can one effectively decide whether two given groups have isomorphic profinite completions? Thanks to Bridson and Wilton, it is known that the answer is `no' in general, even for finitely presented residually finite groups. However, if the groups are (and are given to be) virtually polycyclic, then the answer is 'yes'. This is not really surprising, as a lot is known both about the profinite completions of such groups and about how they are determined up to isomorphism; but it may be instructive to see how it is done.

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