seminar: Subgroups of large girth

speaker: Tal Poznansky (Yale University)

abstract: In the study of finitely generated groups, the notion of girth is a precise analogue of the notion of injectivity radius in the theory of Riemannian manifolds. Tits' alternative can be stated as a characterization of non-virtually solvable groups in terms of geometry. Namely, a finitely generated linear group $\Gamma$ is not virtually solvable if and only if it contains subgroups of arbitrarily large girth. We shall show this is equivalent to the stronger statement that for any nontorsion element $\gamma$ of $\Gamma $ and every number $n$, there exists a partner $h \in \Gamma$ which together with the fixed element $\gamma$ generates a subgroup of girth exceeding $n$.

timetable:
Sun 2 Sep, 18:00 - 19:00, Lizzanello
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