# Determining Defining Relations for a Group

## Homework Statement

Given some group G with generators g$_{1}$,g$_{2}$,...,g$_{n}$ as well as a description of the action of g on the elements of some set S={s$_{1}$,s$_{2}$,...,s$_{k}$}, how in general does one go about finding a complete defining relations (and showing they are complete)?

## Homework Equations

For example, the group of symmetries of an n-gon has generators R (rotation) and D (flip across a diagonal) with defining relations R$^{n}$=1=D$^{2}$ and RD=DR$^{n-1}$. Both R and D can be described by their effect on the vertices of the n-gon.

## The Attempt at a Solution

I understand that the example I gave has a complete set of relations, and it seems to be something of a requirement to show the orders of the generators (if finite) and how any two generators "commute" with one another. Is this at all on track? Is there some general method?