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IMCS/Publications/QRS/Issues/QRS v.16, n.2 (20), 2008/

The action of G22 on PL(Fp)

Authors: Q. Mushtaq and N. Siddiqui

Abstract

K3 is a copy of unique circuit-free connected graph all of whose vertices have degree 3, called cubic tree. The group G22 generated by x, y, t such that x2=t, y3=t2=(yt)2=1, is one of the seven finitely presented isomorphism types of sub\-groups of the full automorphism group Aut(K3) of K3. These seven groups act arc-transitively on the arcs of K3 with a finite vertex stabilizer. In this paper we have found a condition on p such that the action of K3 on the projective line over the finite field, PL(Fp), always yields the subgroups of the alternating groups of degree p+1. We have shown also that the action of K3 on PL(Fp) is transitive.

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