engleski

On the number of primitive designs on projective line and their antifl‡ag-transitivity

We have considered, up to isomorphism and complementation, the construction of primitive block designs on projective line, i.e. designs with an automorphism group acting primitively on both point and block set. For q ≥13, q ≠23 the proved properties can roughly be put as follows. 1. There exist exactly one infinite series of primitive, flag-transitive designs with the base block stabilizer in the second Aschbacher's class, that being for q ≡1(mod 4) ; 2. There exist exactly one in.nite series of primitive, both flag and antiflag- transitive designs with the base block stabilizer in the third Aschbacher's class, that being for q ≡1(mod 4) ; 3. There exist exactly two in.nite series of primitive, both flag and antiflag-transitive designs with the base block stabilizer in the .fth Aschbacher's class. 4. There exist exactly 9 primitive, antiflag-transitive designs with the base block stabilizer in the sixth Aschbacher's class. 5. There exist exactly 8 primitive, antiflag-transitive designs with the base block stabilizer in the ninth Aschbacher's class.

block design; primitive automorphism group; anti‡ag-transitivity

nije evidentirano