Geodesic
On recognizability by spectrum of finite simple groups of types $B_n$, $C_n$, and ${}^2D_n$ for$n=2^k$
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 15 (2009) no. 2, pp. 58-73

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The spectrum of a finite group is the set of its element orders. A group is said to be recognizable (by spectrum) if it is isomorphic to any finite group that has the same spectrum. A nonabelian simple group is called quasirecognizable if every finite group with the same spectrum possesses a unique nonabelian composition factor, and this factor is isomorphic to the simple group in question. We consider the problem of recognizability and quasi-recognizability for finite simple groups of types $B_n$, $C_n$, and ${}^2D_n$ with $n=2^k$.
Keywords: finite simple group, spectrum of a group, prime graph, recognition by spectrum, symplectic group.
Mots-clés : orthogonal group 
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     title = {On recognizability by spectrum of finite simple groups of types $B_n$, $C_n$, and ${}^2D_n$ for$n=2^k$},
     journal = {Trudy Instituta matematiki i mehaniki},
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A. V. Vasil'ev; I. B. Gorshkov; M. A. Grechkoseeva; A. S. Kondrat'ev; A. M. Staroletov. On recognizability by spectrum of finite simple groups of types $B_n$, $C_n$, and ${}^2D_n$ for$n=2^k$. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 15 (2009) no. 2, pp. 58-73. http://geodesic.mathdoc.fr/item/TIMM_2009_15_2_a5/