The Möbius function of the small Ree groups

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• Emilio Pierro, Birkbeck, University of London
• Friday 21 November 2014, 15:00-16:00
• CMS, MR4.

If you have a question about this talk, please contact Julian Brough.

In 1936 Hall showed that Möbius inversion could be applied to the lattice of subgroups of a finite group $G$ in order to determine the number of generating sets of $G$ of size $n$. The related question of considering generating $n$-tuples subject to relations can also be answered with applications to the theory of Riemann surfaces, Hurwitz groups, dessins d’enfants and various other algebraic, topological and combinatorial enumerations. In order to determine the Möbius function of a group it is necessary to understand the subgroup structure of a group and so we also give a description of the simple small Ree groups $R(q)=^{2G_2(q)$, in particular their maximal subgroups, in terms of their 2-transitive permutation representations of degree $q}3+1$.

This talk is part of the Junior Algebra and Number Theory seminar series.

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