nLab
free group

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.

Revised on October 9, 2012 22:09:04 by Urs Schreiber (82.169.65.155)