Flag-transitive 2-(v, k, λ) symmetric designs with (k, λ) = 1 and alternating socle

Classification of the non-trivial 2-$$(v,k,\lambda )$$ designs, with $$ (r,\lambda )=1$$ and $$\lambda >1$$, admitting a non-solvable flag-transitive automorphism group of affine type

“…A complete classification of D is provided in [9] for λ = 1 when G A L 1 (v), v a power of a prime. The case λ > 1 has been investigated by Zhou et al in [36,37], when Soc(G) is alternating, by Zhan and Zhou in [34,35] when Soc(G) is sporadic or isomorphic to P SL (2, q), q = p n > 3, and by Biliotti and Montinaro [6] when D is symmetric and G is of affine type, that is Soc(G) is an elementary abelian pgroup. In the present paper the non-trivial 2-(v, k, λ) designs, with (r , λ) = 1 and λ > 1, admitting a non-solvable flag-transitive automorphism group G of affine type are classified.…”

Flag-Transitive Non-Symmetric 2-Designs with $(r, \lambda)=1$ and Exceptional Groups of Lie Type

“…In [4], P. Dembowski proved that if G is a flag-transitive automorphism group of a 2-design D with (r, λ) = 1, then G is point-primitive and P. H. Zieschang [30] proved that G must be of almost simple or affine type. Such 2-designs have been studied in [1,26,27,28,29], where the socle of G is an elementary abelian p-group, a sporadic group or an alternating group, respectively. In this paper, we continue to study the non-symmetric case that the socle of G is an exceptional simple group of Lie type.…”

Nonsymmetric 2‐(v,k,λ) designs, with (r,λ) = 1, admitting a solvable flag‐transitive automorphism group of affine type

“…A complete classification of is provided in for when , a power of a prime. The case has been investigate by Zhou et al in and when is alternating, by Zhan and Zhou in and when is sporadic or isomorphic to , and by Biliotti and Montinaro when is symmetric and of affine type, that is is an elementary abelian ‐group. The present paper and are devoted to the study of nonsymmetric designs with admitting a flag‐transitive automorphism group of affine type according to whether is solvable or not, respectively.…”