10
votes
0answers
233 views

Generating random finite groups

I would like a method to efficiently generate a random finite group of a given order $n$. If there are $g(n)$ non-isomorphic groups of order $n$, ideally each group would occur with probability ...
3
votes
2answers
344 views

The cycle structure of twisted wires, connected

Suppose you have $n$ (blue) wires linearly arrayed at junction box $A$, connected to a remote junction box $B$, where the wires are now arrayed along a line in a randomly permuted order, i.e., each ...
12
votes
4answers
1k views

Has any attempt been made to classify finite groupoids?

I recently stumbled upon the Mathieu groupoid and I found them fascinating. It appears as a subset of $S_{13}$ which is not closed under multiplication, but it turns out to be a groupoid with 13 ...