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SUMMARY:Mekler constructions in generalized stability
DTSTART;VALUE=DATE-TIME:20170907T083000Z
DTEND;VALUE=DATE-TIME:20170907T093000Z
DTSTAMP;VALUE=DATE-TIME:20190223T190651Z
UID:indico-event-2532@indico.math.cnrs.fr
DESCRIPTION:Given a so called nice graph (no triangles\, no squares\, for
any choice of two distinct vertices there is a third vertex which is conne
cted to one and not the other)\, Mekler considered the 2-nilpotent subgro
up generated by the vertices of the graph in which two elements given by v
ertices commute if and only if there is an edge between them. These groups
form an interesting collection of examples from a model theoretic point o
f view. It was shown that such a group is stable if and only if the corres
ponding graph is stable and Baudisch generalized this fact to the simple t
heory context. In a joint work with Chernikov\, we were able to verify thi
s result for k-dependent and NTP_2 theories. This leads to the existence
of groups which are (k+1)-dependent but not k-dependent\, providing the f
irst algebraic objects witnessing the strictness of these hierarchy.\n\nh
ttps://indico.math.cnrs.fr/event/2532/
LOCATION:La Doua Fokko du Cloux
URL:https://indico.math.cnrs.fr/event/2532/
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