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CATEGORIES:Geometric Group Theory (GGT) Seminar
SUMMARY:The profinite and pro-p genus of free and surface
groups. - Ismael Morales (University of Oxford)
DTSTART;TZID=Europe/London:20230210T134500
DTEND;TZID=Europe/London:20230210T144500
UID:TALK195868AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/195868
DESCRIPTION:Let $S$ be a free or surface group. A finitely gen
erated group $G$ is said to be in the profinite (o
r pro-$p$) genus of $S$ if it is residually-finite
(resp. residually-$p$) and has the same collectio
n of quotients in the class of finite groups (resp
. finite $p$--groups). It is an open question whet
her the profinite genus of S uniquely consists of
the group $S$. Nevertheless\, the pro --$p$ genus
is bigger than the profinite genus in these cases\
, and we will see how this can be used to confirm
a weaker version of the question. We also handle t
he similar case of $S\\times \\mathbb{Z}^n^$. Exte
nding this result to a bigger class of groups woul
d require improvements of Lück's approximation pri
nciples for the $L^2^$ invariants and Gromov's con
jecture about the existence of surface subgroups.
LOCATION:MR13
CONTACT:
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