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Questions on group theory which concern finite groups.
3
votes
General bound for the number of subgroups of a finite group
In a similar vein to Geoff Robinson's answer, observe that any proper subgroup of a group of order $n$ can be generated by at most $\Omega(n) - 1$ elements, where $\Omega$ counts the number of prime f …
23
votes
Accepted
Presentation of the Monster Group
There's a 12-generator 80-relator presentation for the Monster group. Specifically, we have 78 relators for the Coxeter group Y443:
$12$ relators of the form $x^2 = 1$, one for each node in the Coxe …
23
votes
What is the geometric shape of the Monster sporadic group?
In the penultimate chapter of Sphere Packings, Lattices and Groups, the authors define a $196884$-dimensional real vector space and a faithful representation of the Monster group on that space.
Now, …