SPEAKER: Dalen T. Dockery

TITLE: *
Generalized commutator probability for group elements
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In this project, we look at a probabilistic question in group theory: let $G$ be a group with $H$ a subgroup of $G$, and define the commutator of two group elements $x$ and $y$ to be $xyx^{-1}y^{−1}.$ We determine the probability that this commutator lies in $H$ for an arbitrary choice of $x$ and $y$. Additionally, we provide special cases of this probability for certain types of groups $G$ and subgroups $H$, as well as probabilistic bounds for this condition. We conclude by looking at a few interesting questions regarding this probability, particularly its extremes under various conditions.

The semester schedule can be found at: