On locally finite groups saturated by full and special linear groups over finite fields

Every locally finite group saturated by groups from the set of projective special linear groups of a fixed degree over finite fields is known to be isomorphic to the projective special linear group of the given fixed degree over a suitable locally finite field. We describe the locally finite groups saturated by groups from the set of full linear groups and special linear groups of a fixed degree over finite fields. These are either full linear groups or special linear groups of the given fixed degree over a suitable locally finite field.