Prüfer Group

The Prüfer group, also known as the Prüfer p-group, is a special type of mathematical structure called an abelian (commutative) group, focused on a prime number p. It consists of all roots of unity, or complex numbers that, when raised to some power, equal 1, with the order of these roots related to p. Think of it as an infinite collection where every element has p-power roots, and the group is built to study how these roots interact. It serves as an important example in abstract algebra, illustrating properties of divisible and torsion groups.