Geodesic
Recognition by spectrum for finite linear groups over fields of characteristic~2
Algebra i logika, Tome 47 (2008) no. 4, pp. 405-427.

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The spectrum of a finite group is the set of its element orders. For every finite simple linear group $L=L_n(2^k)$, where $11\le n\le18$ or $n>24$, we describe finite groups having the same spectrum as $L$, prove that the number of pairwise nonisomorphic groups with this property is finite, and derive an explicit formula for calculating this number.
Keywords: finite simple group, linear group, order of element, spectrum of group, recognition by spectrum. 
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M. A. Grechkoseeva. Recognition by spectrum for finite linear groups over fields of characteristic~2. Algebra i logika, Tome 47 (2008) no. 4, pp. 405-427. http://geodesic.mathdoc.fr/item/AL_2008_47_4_a0/

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