Category:Definitions/Group Presentations

This category contains definitions related to Group Presentations.
Related results can be found in Category:Group Presentations.

Let $G$ be a group.

A (group) presentation for $G$ is a definition in the form:

$G = \gen {a_1, a_2, \ldots, a_n: w_1 = e, w_2 = e, \ldots, w_k = e}$

where:

$a_1, a_2, \ldots, a_n$ is a list of generators of $G$

$w_1 = e, w_2 = e, \ldots, w_k = e$ is a list of equations specifying relations between powers of these generators.