nLab
free group

Contents

Contents

Idea

The free group on a given set SS is the free object on SS in the category of groups. The elements of SS are called the generators of this group.

Properties

Every subgroup of a free group is itself a free group. This is the Nielsen-Schreier theorem.

Last revised on October 9, 2012 at 22:09:04. See the history of this page for a list of all contributions to it.