On Recognition of the Finite Simple Orthogonal Groups of Dimension 2m, 2m+1, and 2m+2 over a Field of Characteristic 2

The spectrum (G) of a finite group G is the set of element orders of G. A finite group G is said to be recognizable by spectrum (briefly, recognizable) if HG for every finite group H such that (H)=(G). We give two series, infinite by dimension, of finite simple classical groups recognizable by spectrum.