Dear Thomas,
Thank you for your helpful comments on calculating the symmetrised structure constant. Perhaps my understanding of rational classes is incorrect, but I have taken it from this equivalence: https://math.stackexchange.com/questions/218302/a-conjugacy-class-c-is-rational-iff-cn-in-c-whenever-c-in-c-and-n-is-co >From my understanding of that, we would say a conjugacy class is rational if >every entry of it in the character table is rational under the respective >column. However, using my reasoning, if we look at M11, under the columns 8a >and 8b it has entries of A = -sqrt(-2) and also underneath 11a and 11b it has >entries B = (-1 - sqrt(-11)/2) both which are not rational and so that would >mean M11 has only 6 rational classes (it has a total of 10 conjugacy classes) But, using the "RationalClasses" function on GAP we know that M11 has 8 rational classes. I'm certain I am mistaken in my reasoning/interpretation of the character table and would very much be appreciative of an explanation. 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. I am very much appreciative for all your help, John [https://cdn.sstatic.net/Sites/math/img/apple-touch-i...@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> 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 ... Sent from Outlook<http://aka.ms/weboutlook> _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
