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Quasirecognition by Prime Graph of the Groups 2D2n(q) Where q < 105

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Department of Mathematics, Tarbiat Modares University, P.O. Box 14115-137, Tehran, Iran
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School of mathematics, statistics and computer, College of science, University of Tehran, P.O. Box 14155-6455, Tehran, Iran
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Author to whom correspondence should be addressed.
Mathematics 2018, 6(4), 57; https://doi.org/10.3390/math6040057
Received: 8 January 2018 / Revised: 8 March 2018 / Accepted: 14 March 2018 / Published: 9 April 2018
Let G be a finite group. The prime graph Γ ( G ) of G is defined as follows: The set of vertices of Γ ( G ) is the set of prime divisors of | G | and two distinct vertices p and p are connected in Γ ( G ) , whenever G contains an element of order p p . A non-abelian simple group P is called recognizable by prime graph if for any finite group G with Γ ( G ) = Γ ( P ) , G has a composition factor isomorphic to P. It is been proved that finite simple groups 2 D n ( q ) , where n 4 k , are quasirecognizable by prime graph. Now in this paper we discuss the quasirecognizability by prime graph of the simple groups 2 D 2 k ( q ) , where k 9 and q is a prime power less than 10 5 . View Full-Text
Keywords: prime graph; simple group; orthogonal groups; quasirecognition prime graph; simple group; orthogonal groups; quasirecognition
MDPI and ACS Style

Moradi, H.; Darafsheh, M.R.; Iranmanesh, A. Quasirecognition by Prime Graph of the Groups 2D2n(q) Where q < 105. Mathematics 2018, 6, 57.

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