Abstract
The group is important because it is one of the seven finitely presented isomorphism types of subgroups of the full automorphism group (Aut(Γ3)) of a cubic tree Γ3. These seven groups act arc-transitively on the arcs of Γ3 with a finite vertex stabilizer. In this article, we have parametrized the actions of on the projective line over the finite field, PL(F p ), where p is the Pythagorean prime and has thus shown that there is only one coset diagram depicting the sole conjugacy class of these actions.
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