“School of Mathematics”
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| Paper IPM / M / 8119 |
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| Abstract: | |||||||
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The group \PGL(2,q), q=pn, p an odd prime, is
3-transitive on the projective line and therefore it can be
used to construct 3-designs. In this paper, we determine the
sizes of orbits from the action of \PGL(2,q) on the k-subsets
of the projective line when k is not congruent to 0 and 1
modulo p. Consequently, we find all values of λ for
which there exist 3-(q+1,k,λ) designs admitting
\PGL(2,q) as automorphism group. In the case p ≡ 3 mod 4,
the results
and some previously known facts are used
to classify 3-designs from \PSL(2,p) up to isomorphism.
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