google-deepmind / google-deepmind/formal-conjectures
Erdős Problem 117: cover group with a minimal number of Abelian subgroups
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ams-20 Group theory and generalizations
erdos-problems
new conjecture
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Description
### What is the conjecture
https://www.erdosproblems.com/117
Let $h(n)$ be minimal such that any group $G$ with the property that any subset of $>n$ elements contains some $x\neq y$ such that $xy=yx$ can be covered by at most $h(n)$ many Abelian subgroups. Estimate $h(n)$ as well as possible.
Status: open
### Choose either option
- [ ] I plan on working on this conjecture
- [x] This issue is up for grabs: I would like to see this conjecture added by somebody else
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