On Recognizability by Spectrum of Finite Simple Groups of Types Bn, Cn, and 2Dn for n=2k

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 quasi-recognizable 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 D-2(n) with n = 2(k).