Recognizability of groups \(G_2(q)\) by spectrum.

DOI10.1007/s10469-013-9214-0zbMath1284.20012OpenAlexW192237053MaRDI QIDQ354485

Alexey Mikhailovich Staroletov, Andrey V. Vasilev

Publication date: 19 July 2013

Published in: Algebra and Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10469-013-9214-0

zbMATH Keywords

finite simple groupsprime graphsrecognition by spectrasets of element ordersspectra of groupsrecognizable groupsGruenberg-Kegel graphssimple groups of type \(G_2\)

Mathematics Subject Classification ID

Linear algebraic groups over finite fields (20G40) Arithmetic and combinatorial problems involving abstract finite groups (20D60) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Simple groups: alternating groups and groups of Lie type (20D06)

Related Items (14)

Spectra of automorphic extensions of finite simple exceptional groups of Lie type ⋮ Codegrees and element orders of almost simple groups ⋮ Element orders in covers of finite simple groups. ⋮ Automorphism Orbits and Element Orders in Finite Groups: Almost-Solubility and the Monster ⋮ Finite groups isospectral to simple groups ⋮ Spectra of the finite simple groups \(E_{7}(q)\) ⋮ On recognizability of \(\mathrm{PSU}_3(q)\) by the orders of maximal abelian subgroups ⋮ Spectra of groups \(E_8(q)\) ⋮ On finite groups isospectral to the simple groups \(S_4(q)\) ⋮ Recognition of symplectic and orthogonal groups of small dimensions by spectrum ⋮ An OD-Characterizable Class of Simple Groups ⋮ Element orders in covers of finite simple groups of Lie type ⋮ Recognition by spectrum for simple classical groups in characteristic 2. ⋮ Almost recognizability by spectrum of simple exceptional groups of Lie type.

Cites Work

• Sporadic composition factors of finite groups isospectral to simple groups.
• Recognition by spectrum for finite simple groups of Lie type.
• Prime graph components of finite groups
• Prime power graphs for groups of Lie type
• An Adjacency Criterion for the Prime Graph of a Finite Simple Group
• The cyclic structure of maximal tori of the finite classical groups
• On Zsigmondy primes
• Finite simple unisingular groups of Lie type
• Recognition of the simple groups L3(q) by element orders
• Recognition of finite groups by the prime graph
• FIXED VECTORS FOR ELEMENTS IN MODULES FOR ALGEBRAIC GROUPS
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