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The $h$-fold product set of $A$ is defined as $$A^{h} :=\\lbrace a_{1}.a_{2}...a_{h} : a_{1},\\ldots,a_n \\in A \\rbrace.$$ Nathanson considered the concept of an asymptotic approximate group. Let $r,l \\in \\mathbb{N}$. The set $A$ is said to be an $(r,l)$ approximate group in $G$ if there exists a subset $X$ in $G$ such that $|X|\\leqslant l$ and $A^{r}\\subseteq XA$. 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