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- W4287823488 abstract "A Hurwitz generating triple for a group $G$ is an ordered triple of elements $(x,y,z) in G^3$ where $x^2=y^3=z^7=xyz=1$ and $langle x,y,z rangle = G$. For the finite quasisimple exceptional groups of types $F_4$, $E_6$, $^2E_6$, $E_7$ and $E_8$, we provide restrictions on which conjugacy classes $x$, $y$ and $z$ can belong to if $(x,y,z)$ is a Hurwitz generating triple. We prove that there exist Hurwitz generating triples for $F_4(3)$, $F_4(5)$, $F_4(7)$, $F_4(8)$, $E_6(3)$ and $E_7(2)$, and that there are no such triples for $F_4(2^{3n-2})$, $F_4(2^{3n-1})$, $E_6(7^{3n-2})$, $E_6(7^{3n-1})$, $SE_6(7^n)$ or $^2E_6(7^n)$ when $n geq 1$." @default.
- W4287823488 created "2022-07-26" @default.
- W4287823488 creator A5042902838 @default.
- W4287823488 date "2020-03-27" @default.
- W4287823488 modified "2023-09-27" @default.
- W4287823488 title "Hurwitz Generation in Groups of Types $F_4$, $E_6$, $^2E_6$, $E_7$ and $E_8$" @default.
- W4287823488 doi "https://doi.org/10.48550/arxiv.2003.12595" @default.
- W4287823488 hasPublicationYear "2020" @default.
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