Automorphism groups of designs with $λ=1$

William M. Kantor

Published 2018-05-30Version 1

If $G$ is a finite group and $k =q>2$ or $k=q+1$ for a prime power $q$ then, for infinitely many integers $v$, there is a $2$--$(v,k,1)$-design ${\bf D}$ for which ${\rm Aut} {\bf D}\cong G$. For each prime power $q > 7$ there is a design ${\bf D}$ having the parameters of the point-line design of ${\rm PG}(3,q)$ and for which ${\rm Aut} {\bf D}=1$.