Flag-transitive, point-imprimitive 2-(v, k, λ) symmetric designs with k and λ prime powers

作者：Chen, Jianfu; Zhou, Shenglin^*

来源：Designs, Codes, and Cryptography, 2021, 89(6): 1255-1260.

DOI：10.1007/s10623-021-00869-5

• Symmetric design
• Automorphism group
• Flag-transitive
• Primitivity

Let D be a 2-(v, k, lambda) symmetric design with k and lambda prime powers. If D admits a flag-transitive, point-imprimitive automorphism group G, we show that both k and lambda must be powers of 2. Moreover, there exists an integer m such that either (a) D has parameters (v, k, lambda)=(2(2m+2) - 1, 2(2m+1), 2(2m)), and G preserves a partition of the points into 2(m+1) + 1 classes of size 2(m+1) - 1, or (b) D has parameters (v, k, lambda) = ((2(2m-1) - 2(m) + 1)(2(m-1) + 1), 2(2m-1), 2(m)), and G preserves a partition of the points into 2(2m-1) - 2(m) + 1 classes of size 2(m-1) + 1.