3-Designs from PSL(2, q)
نویسندگان
چکیده
The group PSL(2, q) is 3-homogeneous on the projective line when q is a prime power congruent to 3 modulo 4 and therefore it can be used to construct 3-designs. In this paper, we determine all 3-designs admitting PSL(2, q) with block size not congruent to 0 and 1 modulo p where q = pn.
منابع مشابه
Simple 3-designs and PSL(2, q) with q == 1 (mod 4)
In this paper, we consider the action of (2, q) on the finite projective line Fq ∪ {∞} for q ≡ 1 (mod 4) and construct several infinite families of simple 3-designs which admit PSL(2, q) as an automorphism group. Some of the designs are also minimal. We also indicate a general outline to obtain some other algebraic constructions of simple 3-designs.
متن کامل3-Designs with block size 6 from PSL(2, q) and their large sets
We investigate the existence of 3-designs and uniform large sets of 3-designs with block size 6 admitting PSL(2, q) as an automorphism group. We show the existence of simple 3-(28, 6, 10m) designs for 1 ≤ m ≤ 230. Most of these designs were previously unknown.
متن کاملFlag-transitive Point-primitive Symmetric Designs and Three Dimensional Projective Special Linear Groups
The main aim of this article is to study (v, k, λ)-symmetric designs admitting a flag-transitive and point-primitive automorphism group G whose socle is PSL(3, q). We indeed show that the only possible design satisfying these conditions is a Desarguesian projective plane PG(2, q) and G ⩾ PSL(3, q).
متن کاملFlag-transitive Point-primitive symmetric designs and three dimensional projective special linear groups
The main aim of this article is to study (v,k,λ)-symmetric designs admitting a flag-transitive and point-primitive automorphism group G whose socle is PSL(3,q). We indeed show that the only possible design satisfying these conditions is a Desarguesian projective plane PG(2,q) and G > PSL(3,q).
متن کامل3-Designs from PGL(2, q)
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,...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Discrete Mathematics
دوره 306 شماره
صفحات -
تاریخ انتشار 2006