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Results tagged with finite-groups
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user 39521
Questions on group theory which concern finite groups.
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, …
- 12.4k
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 …
- 12.4k
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 …
- 12.4k