Behrooz Khosravi
Hossein Moradi - Amirkabir University of Technology

‎Let G be a finite group‎. ‎In [Ghasemabadi et al.‎, ‎characterizations of the simple group {}^۲D_n(۳) by prime graph‎ ‎and spectrum‎, ‎Monatsh Math.‎, ‎۲۰۱۱] it is‎ ‎proved that if n is odd‎, ‎then {}^۲D _n(۳) is recognizable by‎ ‎prime graph and also by element orders‎. ‎In this paper we prove‎ ‎that if n is even‎, ‎then D={}^۲D_{n}(۳) is quasirecognizable by‎ ‎prime graph‎, ‎i.e‎. ‎every finite group G with \Gamma(G)=\Gamma(D)‎ ‎has a unique nonabelian composition factor and this factor is isomorphic to‎ ‎D‎.

prime graph, simple group, linear group, quasirecognition