On recognizability by spectrum of finite simple groups of types $B_n$, $C_n$, and ${}^2D_n$ for$n=2^k$

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 $n=2^k$.