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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 …
Adam P. Goucher's user avatar
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 …
Adam P. Goucher's user avatar
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, …
Adam P. Goucher's user avatar