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

2021/10/18 by Antonina P. Khramova, Н. В. Маслова, Khramova, A. P. +5
Computer Science · Engineering · Mathematics · #20D06 #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2110.09175

openalex publication_date 2021/10/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Gruenberg--Kegel graph (or the prime graph) Γ(G) of a finite group G is defined 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 finite group such that Γ(G)=Γ(L), then G≅ L.

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