Groups Obtained from $2-(n,4,3)$ Supersimple Designs

Abstract

We contribute towards the classification programme for Conway groupoids associated to a $2-(n,4,\lambda )$ design. Our main results improve the known bounds for a hole stabilizer to be primitive, or to contain the alternating group, $\mathrm{Alt}(n-1)$. We exploit these improved bounds to give a partial classification for Conway groupoids when $\lambda =3$.

10 pages