on almost recognizability by spectrum of simple classical groups

‎the set of element orders of a finite group $g$ is called the {em spectrum}‎. ‎groups with coinciding spectra are said to be {em isospectral}‎. ‎it is known that if $g$ has a nontrivial normal soluble subgroup then there exist infinitely many pairwise non-isomorphic‎ ‎groups isospectral to $g$‎. ‎the situation is quite different if $g$ is a nonabelain simple group‎. ‎recently it was proved that if $l$ is a simple classical group of dimension at least 62 and $g$ is a finite group‎ ‎isospectral to $l$‎, ‎then up to isomorphism $lleq gleqaut l$‎. ‎we show that the assertion remains true‎ ‎if 62 is replaced by 38‎.