$3$-Designs from PGL$(2,q)$

P. J. Cameron, G. R. Omidi, B. Tayfeh-Rezaie

doi:10.37236/1076

$3$-Designs from PGL$(2,q)$

DOI Web Site 被引用文献1件

書誌事項

公開日: 2006-05-19

DOI

10.37236/1076

公開者: The Electronic Journal of Combinatorics

説明

<jats:p>The group PGL$(2,q)$, $q=p^n$, $p$ 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 $\lambda$ for which there exist $3$-$(q+1,k,\lambda)$ designs admitting PGL$(2,q)$ as automorphism group. In the case $p\equiv 3$ mod 4, the results and some previously known facts are used to classify 3-designs from PSL$(2,p)$ up to isomorphism.</jats:p>