Free, open-source online mathematics for students, teachers and workers

First Sylow Theorem: The group $G$ contains at least one subgroup of order $p^m$

Second Sylow Theorem: Any two subgroups of $G$ of order $p^m$ are conjugate

Third Sylow Theorem: The number of subgroups of $G$ of order $p^m$ is congruent to $1$ modulo $p$ and is a factor of $k$