**Title**: Residual Finiteness of solvable groups and distortion of cyclic subgroups

**Speaker**: Mark Pengitore (Ohio state University)

**Abstract**: We provide polynomial lower bounds for residual finiteness of residually finite, finitely generated solvable groups that admit infinite order elements in the Fitting subgroup of strict distortion at least exponential. For this class of solvable groups which include polycyclic groups with a nontrivial exponential radical and the metabelian Baumslag-Solitar groups, we improve the lower bounds found in the literature. Additionally, for the class of residually finite, finitely generated solvable groups of infinite Prüfer rank that satisfy the conditions of our theorem, we provide the first nontrivial lower bounds.

**Seminar URL**: https://research.math.osu.edu/ggt/