Shunkov groups saturated by general linear groups of degree 3

Saturation and the related concept of a saturating set are among the finiteness conditions for infinite groups. Saturation is applied to studying periodic groups and Shunkov groups with saturating sets consisting of finite simple nonabelian groups. This article addresses periodic Shunkov groups with saturating sets consisting of groups of a larger class. We establish the structure of a periodic Shunkov group saturated by the general linear groups of degree 3 over finite fields of characteristic 2.