My steps created matrices. The group PGL is implemented as a group of 
permutations.

I can make my question more accurate:

I have a (symmetric) set of 2x2 matrices S over Fq. How can I find the 
spectrum of the Cayley graph of PGL(2,q) with respect to the set of 
generators S?
 

On Monday, April 7, 2014 9:16:28 PM UTC+3, David Joyner wrote:
>
> On Mon, Apr 7, 2014 at 11:36 AM, Oren Becker 
> <oren....@gmail.com<javascript:>> 
> wrote: 
> > I would like to compute the spectrum of a certain Cayley graph on 
> PGL(2,q), for a certain prime power q. 
> > 
> > I created the generators of the graph as elements of GL(2,q). 
> > 
>
> Why don't you redo your steps but change this step to use PGL instead of 
> GL? 
>
> > Now, how do I get the spectrum of the Cayley graph on PGL(2,q)? I 
> thought to first create the Cayley graph using PGL.cayley_graph(), and then 
> take the spectrum. But, taking a quotient is not implemented on GL(2,q), so 
> I can't even move from GL to PGL. 
> > 
> > Of course, I can work hard to create the adjacency matrix, then take the 
> spectrum, but I'm hoping for an easier solution. 
> > 
> > (I am new to Sage). 
> > 
> > Thanks, 
> > Oren. 
> > 
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