Geodesic
Recognition by spectrum for finite simple linear groups of small dimensions over fields of characteristic 2
Algebra i logika, Tome 47 (2008) no. 5, pp. 558-570

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Two groups are said to be isospectral if they share the same set of element orders. For every finite simple linear group $L$ of dimension $n$ over an arbitrary field of characteristic 2, we prove that any finite group $G$ isospectral to $L$ is isomorphic to an automorphic extension of $L$. An explicit formula is derived for the number of isomorphism classes of finite groups that are isospectral to $L$. This account is a continuation of the second author's previous paper where a similar result was established for finite simple linear groups $L$ in a sufficiently large dimension ($n>26$), and so here we confine ourselves to groups of dimension at most 26.
Keywords: finite simple group, linear group, order of element, spectrum of group, recognition by spectrum. 
@article{AL_2008_47_5_a2,
     author = {A. V. Vasil'ev and M. A. Grechkoseeva},
     title = {Recognition by spectrum for finite simple linear groups of small dimensions over fields of characteristic~2},
     journal = {Algebra i logika},
     pages = {558--570},
     publisher = {mathdoc},
     volume = {47},
     number = {5},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2008_47_5_a2/}
}
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A. V. Vasil'ev; M. A. Grechkoseeva. Recognition by spectrum for finite simple linear groups of small dimensions over fields of characteristic 2. Algebra i logika, Tome 47 (2008) no. 5, pp. 558-570. http://geodesic.mathdoc.fr/item/AL_2008_47_5_a2/