Talk:Approximate group

1-approximate subgroups aren't necessarily subgroups

Here is a counterexample to the statement that "a 1-approximate subgroup is the same thing as a genuine subgroup": Take $G = F_2$ the free group on two generators $a, b$, and $A = \{ba^nb^{-1} | n\text{ odd}\}$. Then $A$ is symmetric, non-empty and $A^2 = (bab^-1)A$, but $A$ isn't a subgroup. Could someone clarify what the precise definition of an approximate subgroup is supposed to be? For now, I have fixed the statement by adding the assumption that $A$ is finite. Astaulphe (talk) 18:45, 17 December 2024 (UTC)