3
$\begingroup$

As a follow-up to the construction of a graph that $S_6$ acts on in Constructing a graph based on numbers of vertices, incident edges, and incident triangles, I am now specifically looking at the relationship between the 6 sets of sets of 5 disjoint 2-cycles (ie $\{(ab),(ac),(ad),(ae),(af)\}$ to the 3 sets of 5 pairwise disjoint 2-cycle triangles (ie $\{\{(ab),(cd),(ef)\},\{(ac),(be),(df)\},\{(ad),(bf),(ce)\},\{((ae),(bd),(cf)\},\{(af),(bc),(de)\}\}$. I think it's important that $\frac{6}{3} =2$ but I am still a bit lost on how to construct an outer automorphism from this info. I would appreciate it if someone could steer me in the right direction.

  • 0
    It's difficult to try and figure out what you are expected to do from isolated individual queries. What was the point of the construction of the graph with 15 vertices? I assumed that you be using that in some way to help you construct the outer automorphism.2012-10-24

1 Answers 1