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\iteman{io-port 06064354}
\itemau{Mushtaq, Qaiser; Siddiqui, Nasir}
\itemti{Parametrization of actions of the automorphism subgroup of a cubic tree on $\text{PL}(\Bbb F_p)$.}
\itemso{Commun. Algebra 40, No. 6, 2106-2114 (2012).}
\itemab
Summary: The group $G_2^2=\langle x,y,t:x^2=t,\ y^3=t^2=(yt)^2=1\rangle$ is important because it is one of the seven finitely presented isomorphism types of subgroups of the full automorphism group ($\Aut(\Gamma_3)$) of a cubic tree $\Gamma_3$. These seven groups act arc-transitively on the arcs of $\Gamma_3$ with a finite vertex stabilizer. In this article, we parametrize the actions of $G_2^2$ on the projective line over the finite field, $\text{PL}(\Bbb F_p)$, where $p$ is the Pythagorean prime and thus show that there is only one coset diagram depicting the sole conjugacy class of these actions.
\itemrv{~}
\itemcc{}
\itemut{cubic trees; subgroups of full automorphism groups; arc-transitivity; vertex stabilizers; actions on projective lines; finite fields; coset diagrams}
\itemli{doi:10.1080/00927872.2011.572266}
\end