TY - JOUR

T1 - On flag-transitive 2-(v,k,2) designs

AU - Devillers, Alice

AU - Liang, Hongxue

AU - Praeger, Cheryl E.

AU - Xia, Binzhou

PY - 2021/1

Y1 - 2021/1

N2 - This paper is devoted to the classification of flag-transitive 2-(v,k,2) designs. We show that apart from two known symmetric 2-(16,6,2) designs, every flag-transitive subgroup G of the automorphism group of a nontrivial 2-(v,k,2) design is primitive of affine or almost simple type. Moreover, we classify the 2-(v,k,2) designs admitting a flag transitive almost simple group G with socle PSL(n,q) for some n≥3. Alongside this analysis we give a construction for a flag-transitive 2-(v,k−1,k−2) design from a given flag-transitive 2-(v,k,1) design which induces a 2-transitive action on a line. Taking the design of points and lines of the projective space PG(n−1,3) as input to this construction yields a G-flag-transitive 2-(v,3,2) design where G has socle PSL(n,3) and v=(3n−1)/2. Apart from these designs, our classification yields exactly one other example, namely the complement of the Fano plane.

AB - This paper is devoted to the classification of flag-transitive 2-(v,k,2) designs. We show that apart from two known symmetric 2-(16,6,2) designs, every flag-transitive subgroup G of the automorphism group of a nontrivial 2-(v,k,2) design is primitive of affine or almost simple type. Moreover, we classify the 2-(v,k,2) designs admitting a flag transitive almost simple group G with socle PSL(n,q) for some n≥3. Alongside this analysis we give a construction for a flag-transitive 2-(v,k−1,k−2) design from a given flag-transitive 2-(v,k,1) design which induces a 2-transitive action on a line. Taking the design of points and lines of the projective space PG(n−1,3) as input to this construction yields a G-flag-transitive 2-(v,3,2) design where G has socle PSL(n,3) and v=(3n−1)/2. Apart from these designs, our classification yields exactly one other example, namely the complement of the Fano plane.

KW - 2-design

KW - Aschbacher classification of finite linear groups

KW - Flag-transitive design

KW - Point-imprimitive design

KW - Primitive permutation group

KW - Projective linear group

UR - http://www.scopus.com/inward/record.url?scp=85089729807&partnerID=8YFLogxK

U2 - 10.1016/j.jcta.2020.105309

DO - 10.1016/j.jcta.2020.105309

M3 - Article

AN - SCOPUS:85089729807

VL - 177

JO - Journal of Combinatorial Theory Series A

JF - Journal of Combinatorial Theory Series A

SN - 0021-9800

M1 - 105309

ER -