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If it turns out that a problem is equivalent to a known open problem, then the open-problem tag is added. After that, the question essentially becomes, "What is known about this problem? What are some possible ways to approach this problem? What are some ways that people have tried to attack it before, and with what results?"
14
votes
A group-theoretic perspective on Frankl's union closed problem
In a somewhat different direction from Alireza: the conjecture is true for a large family of groups, including all abelian groups and many supersolvable groups.
Let me start with the abelian case. P …
6
votes
Generating random finite groups
Are you running computer experiments to verify conjectures? If so, the GAP SmallGroups library will give you exactly what you want up to $n = 1023$.
For example, the GAP commands
n:=16;; G:=SmallGr …