Quasirecognition by prime graph of finite simple groups ${}^2D_n(3)$

Document Type: Research Paper

Authors

Amirkabir University of Technology

Abstract

‎Let $G$ be a finite group‎. ‎In [Ghasemabadi et al.‎, ‎characterizations of the simple group ${}^2D_n(3)$ by prime graph‎ ‎and spectrum‎, ‎Monatsh Math.‎, ‎2011] it is‎ ‎proved that if $n$ is odd‎, ‎then ${}^2D _n(3)$ is recognizable by‎ ‎prime graph and also by element orders‎. ‎In this paper we prove‎ ‎that if $n$ is even‎, ‎then $D={}^2D_{n}(3)$ 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 ‎$D$‎.

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