Symmetric 1-designs from PGL2(q), for q an odd prime power

Symmetric 1-designs from PGL2(q), for q an odd prime power

All non-trivial point and block-primitive 1-(v, k, k) designs that admit the group G = PGL2(q), where q is a power of an odd prime, as a permutation group of automorphisms are determined. These self-dual and symmetric 1-designs are constructed by defining { |M|/|M ∩ Mg|: g ∈ G } to be the set of orb...

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Veröffentlicht in:Glasnik matematički 2021-06, Vol.56 (1), p.1-15
Hauptverfasser: Mbaale, Xavier, Rodrigues, Bernardo Gabriel
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Symmetric designs, linear code, projective general linear group
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description All non-trivial point and block-primitive 1-(v, k, k) designs that admit the group G = PGL2(q), where q is a power of an odd prime, as a permutation group of automorphisms are determined. These self-dual and symmetric 1-designs are constructed by defining { |M|/|M ∩ Mg|: g ∈ G } to be the set of orbit lengths of the primitive action of G on the conjugates of M.
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subjects Symmetric designs, linear code, projective general linear group
title Symmetric 1-designs from PGL2(q), for q an odd prime power
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