[GAP Forum] Cayley diagrams for general groups

[Dimitris Schinianakis]

Dear all,

I'm a beginner in group theory, currently trying to solve all the material
in the "A Book of abstract Algebra", by Pinter.

I'd like to use Sage to verify some of the solutions but also to experiment
a little bit with Cayley Diagrams.

1) Is there a way to draw a Cayley diagram in Sage by defining the group
and the equations for the generators? For example let
G={e,a,b,b^2,b^3,ab,ab^2,ab^3} and the generators satisfy a^2=e, b^4=e,
ba=ab^2. e is of course the identity element.

2) I have a Cayley diagram with no labels, only connections and points are
depicted. I need to create the group table. How can I be sure that my table
is correct? Does a cayley diagram correspond always to only one group?

Regards
Dimitris