Sylow Theorems

When cracking open the structure of a group, it is a useful plan to start with investigating the subgroups of prime order. The Sylow theorems are a set of results which provide us with just the sort of information we need.

Ludwig Sylow was a Norwegian mathematician who established some important facts on this subject. The name is pronounced something like "Soolof".

There is no standard numbering for the Sylow Theorems. Different authors use different labellings. Therefore, the following nomenclature is to a greater or lesser extent arbitrary.