On alternating subgroup $A_5$ in autotopism group of finite semifield plane

We discuss well-known hypothesis that the full collineation group of any finite non-Desarguesian semifield plane is solvable. We continue to investigate the semifield planes of odd order which admit an autotopism subgroup isomorphic to alternating group $A_5$. It is proved that a semifield plane of any odd order does not admit $A_5$ in autotopism group.