Automorphism groups of Steiner triple systems

Abstract

If $G$ is a finite group then there is an integer $M_G$ such that$,$ for $u\ge M_G$ and $u\equiv 1$ or $3$ (mod 6), there is a Steiner triple system $U$ on $u$ points for which $\mathrm{Aut}U\cong G.$ If $V$ is a Steiner triple system then there is an integer $N_V$ such that$,$ for $u\ge N_V$ and $u\equiv 1$ or $3$ $($mod $6),$ there is a Steiner triple system $U$ on $u$ points having $V$ as an $\mathrm{Aut}U$-invariant subsystem such that $\mathrm{Aut}U\cong \mathrm{Aut}V$ and $\mathrm{Aut}U$ induces $\mathrm{Aut}V$ on $V$.