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SUMMARY:The profinite and pro-p genus of free and surface groups. - Ismael
  Morales (University of Oxford)
DTSTART:20230210T134500Z
DTEND:20230210T144500Z
UID:TALK195868@talks.cam.ac.uk
CONTACT:76015
DESCRIPTION:Let $S$ be a free or surface group. A finitely generated group
  $G$ is said to be in the profinite (or pro-$p$) genus of $S$ if it is res
 idually-finite (resp. residually-$p$) and has the same collection of quoti
 ents in the class of finite groups (resp. finite $p$--groups). It is an op
 en question whether the profinite genus of S uniquely consists of the grou
 p $S$. Nevertheless\, the pro --$p$ genus is bigger than the profinite gen
 us in these cases\, and we will see how this can be used to confirm a weak
 er version of the question. We also handle the similar case of $S\\times \
 \mathbb{Z}^n^$. Extending this result to a bigger class of groups would re
 quire improvements of Lück's approximation principles for the $L^2^$ inva
 riants and Gromov's conjecture about the existence of surface subgroups.
LOCATION:MR13
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