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## Homework Statement

Given some group G with generators g[itex]_{1}[/itex],g[itex]_{2}[/itex],...,g[itex]_{n}[/itex] as well as a description of the action of g on the elements of some set S={s[itex]_{1}[/itex],s[itex]_{2}[/itex],...,s[itex]_{k}[/itex]}, 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[itex]^{n}[/itex]=1=D[itex]^{2}[/itex] and RD=DR[itex]^{n-1}[/itex]. 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?