Let $h(n)$ be minimal such that any group $G$ with the property that any subset of $>n$ elements contains some $x\ne y$ such that $xy=yx$ can be covered by at most $h(n)$ many Abelian subgroups.Estimate $h(n)$ as well as possible.

gpt-erdos · GPT-5.2 Pro + Deep Research · unverified

* (\omega(G)) = the largest size of a set (S\subseteq G) with **no two distinct elements commuting** (a “pairwise non‑commuting” set). * $c(G)$ = the **smallest** number of abelian subgroups whose union is $G$.

llm-hunter · gpt pro 5.2 · unverified

1 LLM attack(s) recorded (gpt pro 5.2); unverified.