ABSTRACT
Preview Activity 32.1. In this activity, we will introduce three important theorems known as the
Sylow theorems. In order to understand the Sylow theorems, we will first need to understand con-
jugacy, defined formally as follows:
Definition 32.2. Let G be a group. The element a ∈ G is conjugate to b ∈ G if there is an element g ∈ G so that a = gbg−1.