论文标题
hurwitz以类型的类型$ f_4 $，$ e_6 $，$^2e_6 $，$ e_7 $和$ e_8 $生成
Hurwitz Generation in Groups of Types $F_4$, $E_6$, $^2E_6$, $E_7$ and $E_8$
论文作者
论文摘要
hurwitz为组$ g $生成三倍的是订购的三重元素$（x，y，z）\ in g^3 $中的$ x^2 = y^3 = z^7 = xyz = xyz = 1 $和$ \ langle x，y，z \ z \ rangle = g $。对于有限的Quasisimple典型组$ f_4 $，$ e_6 $，$^2e_6 $，$ e_7 $和$ e_8 $，我们提供了限制，如果$（x，y，z）$属于$ x $，$ y $和$ y $和$ z $的conjugacy类，$ x $ y $和$ z $，是一个hurwitz生成的三重。我们证明，Hurwitz生成了三倍的$ f_4（3）$，$ f_4（5）$，$ f_4（7）$，$ f_4（8）$，$ e_6（3）$和$ E_7（2）$ $ e_6（7^{3n-2}）$，$ e_6（7^{3n-1}）$，$ se_6（7^n）$或$^2e_6（7^n）$时$ n \ geq 1 $。
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 $n \geq 1$.
