TIFR Mathematics 2025 | Part B | Question: 15

Question

Let $m$ be a positive integer, and $S_{m}$ the symmetric group on $m$ letters. Let $n$ be a positive integer such that for every group $G$ of order $n$, there exists an injective group homomorphism $G \hookrightarrow S_{m}$. Then $m \geqslant n$.