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SUMMARY:The Möbius function of the small Ree groups  - Emilio Pierro\, Bi
 rkbeck\, University of London
DTSTART:20141121T150000Z
DTEND:20141121T160000Z
UID:TALK56394@talks.cam.ac.uk
CONTACT:Julian Brough
DESCRIPTION: In 1936 Hall showed that Möbius inversion could be applied t
 o 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 con
 sidering generating $n$-tuples subject to relations can also be answered w
 ith applications to the theory of Riemann surfaces\, Hurwitz groups\, dess
 ins 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 g
 ive a description of the simple small Ree groups $R(q)=^2G_2(q)$\, in part
 icular their maximal subgroups\, in terms of their 2-transitive permutatio
 n representations of degree $q^3+1$.
LOCATION:CMS\, MR4
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