[GAP Forum] Generating a group from a triple of elements.
Hulpke,Alexander
Alexander.Hulpke at colostate.edu
Sat Aug 19 16:45:13 BST 2017
Dear Forum,
Just a very brief note on one remark:
> Essentially, all I am trying to do is find a triple of conjugacy classes (that are rational) such that a triple (g_1, g_2, g_3) of elements satisfies the rigidity condition of Thompson to realize the group M11 as Galois over Q.
My understanding (for details see the Book on representation theory by Lux and Pahlings, and ultimately — as they refer to it — the book by Malle and Matzat) is that the rigidity criterion only realizes M11 over a number field and further work is needed to obtain a rational realization from this.
Regards,
Alexander Hulpke
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> I am very much appreciative for all your help,
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> John
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>
> [https://cdn.sstatic.net/Sites/math/img/apple-touch-icon@2.png?v=4ec1df2e49b1]<https://math.stackexchange.com/questions/218302/a-conjugacy-class-c-is-rational-iff-cn-in-c-whenever-c-in-c-and-n-is-co>
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> A conjugacy class $C$ is rational iff $c^n\\in C$ whenever ...<https://math.stackexchange.com/questions/218302/a-conjugacy-class-c-is-rational-iff-cn-in-c-whenever-c-in-c-and-n-is-co>
> math.stackexchange.com
> Let $C$ be a conjugacy class of the finite group $G$. Say that $C$ is rational if for each character $\chi: G \rightarrow \mathbb C$ of $G$, for each $c\in C$, we ...
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