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 projectivespecial linear groups of a fixed degree over finite fields is known to be isomorphic to the projectivespecial linear group of the given fixed degree over a suitable locally finite field.We describe the locally finite groups saturated by groups from the setof full linear groups and special linear groups of a fixed degree over finite fields. Theseare either full linear groups or special linear groups of the given fixed degreeover a suitable locally finite field.