Thursday,   November 29,    at 2:00 P.M.  in BR305 (or BR420)

SPEAKER:    Dalen T. Dockery

TITLE:    Generalized commutator probability for group elements

Free refreshments at 1:30 in the Bruner second floor faculty lounge.

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: