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 ۶۲ and G is a finite group‎ ‎isospectral to L‎, ‎then up to isomorphism L\leq G\leq\Aut L‎. ‎We show that the assertion remains true‎ ‎if ۶۲ is replaced by ۳۸‎.

Keywords:

‎Simple classical groups‎ , ‎Element orders‎ , ‎Prime graph of a finite group‎ , ‎Almost recognizable group