RECOGNITION OF FINITE SIMPLE GROUPS L3(2^m) AND U3(2^m) BY THEIR ELEMENT ORDERS

It is proved that a finite group isomorphic to a simple non-Abelian group L3(2^m) or U3(2^m) is, up to isomorphism, recognizable by a set of its element orders. On the other hand, for every simple group S = S4(2^m), there exist infinitely many pairwise non-isomorphic groups G with (omega)(G) = (omega)(S). As a consequence, we present a list of all recognizable finite simple groups G, for which 4t (not belong to) (omega)(G) with t > 1.