On the geometry of subgroups of Suzuki group in finite non-miquelian inversive planes

Abstract

The simple Suzuki group $Sz(2^{2r+1})$ can be considered as a subgroup of the group of collineations of 3-dimensional projective space $PG(3,2^{2r+1})$ over $GF(2^{2r+1})$, fixing the special Tits ovoid $t(\psi )$. This group determines a finite non-miquelian egglike Mobius plane $J(o)$ of order $q$, consisting of points and plane sections f the above ovoid, when $q=2^{2r+1}$. In this paper a detailed picture of geometry of the subgroups of $Sz(2^{2r+1})$ is given with respect to the non-miquelian Mobius plane $S(q)$