Naslov
Primitive Block Designs with Automorphism Group PSL(2, q)

Autori
Braić, Snježana ; Mandić Joško ; Vučičić Tanja

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni

Izvornik
Fq 10 Ghent, The Tenth International Conference on Finite Fields and Their Applications / Scientific committee of Fq 10 - Ghent : Local organizing committee of Fq 10, 2011, 110-110

Skup
Fq 10 Ghent, The Tenth International Conference on Finite Fields and Their Applications

Mjesto i datum
Gent, Belgija, 11.07.2011. - 15.07.2011

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
Symmetric design; automorphism group; primitive group action

Sažetak
A block design we call primitive if it has an automorphism group acting primitively on both point and block set. Taking the projective line X={;∞};∪GF(q) as the set of points, our research aims to determine, up to isomorphism and complementation, all primitive block designs with PSL(2, q) as an automorphism group. The number of such designs we denote by npd(q). In dealing with primitive permutation representations of almost simple groups with socle PSL(2, q) we make use of the study [1] of their maximal subgroups. The obtained designs we describe by their base block (a union of orbits of a block stabilizer) and the full automorphism group. Our results so far include completely solving the problem in case when a block stabilizer is not in the fifth Aschbacher's class (in particular, for q a prime), and assertions such as the following. Lemma 1. Let q>=4. Then npd(q)=0 if and only if q=7, 11, 23 or q=2^r, r a prime. Lemma 2. Let q>=13 and let there exist a block design D, the socle of AutD being PSL(2, q). If the base block stabilizer is in the second Aschbacher's class, then q is congruent to 1(mod4), D is 2-(q+1, (q-1)/2, (q-1)(q-3)/8) design up to complementation, and AutD=PΣL(2, q). [1] M. Giudici, Maximal subgroups of almost simple groups with socle PSL(2, q), arXiv:math/0703685v1 [math.GR], 2007.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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