TY - JOUR

T1 - Characterization of groups E6(3) and 2E6(3) by Gruenberg-Kegel graph

AU - Khramova, A. P.

AU - Maslova, N.

AU - Panshin, V. V.

AU - Staroletov, A. M.

N1 - Publisher Copyright: © 2021 Khramova A.P., Maslova N.V., Panshin V.V., Staroletov A.M. The work is supported by the Mathematical Center in Akademgorodok under the agreement 075-15-2019-1675 with the Ministry of Science and Higher Education of the Russian Federation

PY - 2021

Y1 - 2021

N2 - The Gruenberg Kegel graph (or the prime graph) Γ(G) of a nite group G is de ned as follows. The vertex set of Γ(G) is the set of all prime divisors of the order of G. Two distinct primes r and s regarded as vertices are adjacent in Γ(G) if and only if there exists an element of order rs in G. Suppose that L =≅ E6(3) or L ≅= 2E6(3). We prove that if G is a nite group such that Γ(G) = Γ(L), then G ≅= L.

AB - The Gruenberg Kegel graph (or the prime graph) Γ(G) of a nite group G is de ned as follows. The vertex set of Γ(G) is the set of all prime divisors of the order of G. Two distinct primes r and s regarded as vertices are adjacent in Γ(G) if and only if there exists an element of order rs in G. Suppose that L =≅ E6(3) or L ≅= 2E6(3). We prove that if G is a nite group such that Γ(G) = Γ(L), then G ≅= L.

KW - finite group

KW - simple group

KW - the Gruenberg-Kegel graph

KW - exceptional group of Lie type E-6

KW - EXCEPTIONAL GROUPS

KW - ELEMENT ORDERS

KW - FINITE-GROUPS

KW - PRIME GRAPH

KW - Finite group

KW - The gruenbergkegel graph

KW - Exceptional group of lie type e6

KW - Simple group

UR - http://www.scopus.com/inward/record.url?scp=85123794632&partnerID=8YFLogxK

UR - https://elibrary.ru/item.asp?id=47669599

U2 - 10.33048/semi.2021.18.124

DO - 10.33048/semi.2021.18.124

M3 - Article

VL - 18

SP - 1651

EP - 1656

JO - Сибирские электронные математические известия

JF - Сибирские электронные математические известия

SN - 1813-3304

IS - 2

M1 - 14

ER -