The First Sylow Theorem states that for a finite group, if a prime number $p$ divides the order of the group, then there exists at least one subgroup of order $p^k$, where $p^k$ is the highest power of $p$ dividing the group's order. This theorem is crucial as it lays the groundwork for understanding the structure of groups by identifying the existence of subgroups associated with specific prime factors of the group's order.
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