Free Groups

Joachim Breitner 📧

June 24, 2010

This is a development version of this entry. It might change over time and is not stable. Please refer to release versions for citations.


Free Groups are, in a sense, the most generic kind of group. They are defined over a set of generators with no additional relations in between them. They play an important role in the definition of group presentations and in other fields. This theory provides the definition of Free Group as the set of fully canceled words in the generators. The universal property is proven, as well as some isomorphisms results about Free Groups.


BSD License


December 11, 2011
Added the Ping Pong Lemma.


Session Free-Groups

Depends on