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- W4287167859 abstract "We introduce the notion of commuting probability, $p(G)$, for an algebraic group $G$. This notion is inspired by the corresponding notions in finite groups and compact groups. The computation of $p(G)$ for reductive groups is readily done using the notion of $z$-classes. We introduce two generalisations of this relation, $iz$-equivalence and $dz$-equivalence. These notions lead us naturally to the notion of a regular element in $G$. Finally, with the help of this notion of regular elements, we compute $p(G)$ for a connected, linear algebraic group $G$. We also compute the set of limit points of the numbers $p(G)$ as $G$ varies over the classes of reductive groups, solvable groups and nilpotent groups." @default.
- W4287167859 created "2022-07-25" @default.
- W4287167859 creator A5080647540 @default.
- W4287167859 date "2021-05-26" @default.
- W4287167859 modified "2023-09-26" @default.
- W4287167859 title "Commuting probability in algebraic groups" @default.
- W4287167859 doi "https://doi.org/10.48550/arxiv.2105.12550" @default.
- W4287167859 hasPublicationYear "2021" @default.
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