Symmetric 2‐(35,17,8) Designs With an Automorphism of Order 2

ABSTRACT The largest prime that can be the order of an automorphism of a 2‐ design is , and all 2‐ designs with an automorphism of order 17 were classified by Tonchev. The symmetric 2‐ designs with automorphisms of an odd prime order were classified in Bouyukliev, Fack and Winne and Crnković and Rukavina. In this paper we give the classification of all symmetric 2‐ designs that admit an automorphism of order . It is shown that there are exactly nonisomorphic such designs. Furthermore, it is shown that the number of nonisomorphic 3‐ designs which have at least one derived 2‐ design with an automorphism of order 2, is .