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Strongly Real Conjugacy Classes in Unitary Groups over Fields of Even Characteristic
Carawan, Tanner N
Carawan, Tanner N
Abstract
An element $g$ of a group $G$ is called strongly real if there is an $s$ in $G$ such that $s^2 = 1$ and $sgs^{-1} = g^{-1}$. It is a fact that if $g$ in $G$ is strongly real, then every element in its conjugacy class is strongly real. Thus we can classify each conjugacy class as strongly real or not strongly real. Gates, Singh, and Vinroot have classified the strongly real conjugacy classes of U$(n, q^2)$ in the case that $q$ is odd. Vinroot and Schaeffer Fry have classified some of the conjugacy classes of U$(n,q^2)$ where $q$ is even. We conjecture the full classification, and under that conjecture provide a generating function for the number of unipotent strongly real conjugacy classes in U$(n,q^2)$. We also give some computational results.
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2018-05-01
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Mathematics