RECOGNITION OF SOME FINITE SIMPLE GROUPS OF TYPE Dn(q) BY SPECTRUM

The spectrum omega(G) of a finite group G is the set of element orders of G. Let L be finite simple group D-n(q) with disconnected Gruenberg-Kegel graph. First, we establish that L is quasi-recognizable by spectrum except D-4(2) and D-4(3), i.e., every finite group G with omega(G) = omega(L) has a unique nonabelian composition factor that is isomorphic to L. Second, for some special series of integers n, we prove that L is recognizable by spectrum, i.e., every finite group G with omega(G) = omega(L) is isomorphic to L.