Recognizability of alternating groups by spectrum.

DOI10.1007/s10469-013-9217-xzbMath1272.20007OpenAlexW1990707111MaRDI QIDQ354487

Ilya B. Gorshkov

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/s10469-013-9217-x

zbMATH Keywords

finite simple groupsalternating groupsprime graphssets of element ordersspectra of groupsrecognizable groupsGruenberg-Kegel graphsrecognizability by spectrum

Mathematics Subject Classification ID

Arithmetic and combinatorial problems involving abstract finite groups (20D60) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Finite simple groups and their classification (20D05) Simple groups: alternating groups and groups of Lie type (20D06)

Related Items (17)

On spectra of almost simple extensions of even-dimensional orthogonal groups ⋮ Finite simple groups that are not spectrum critical ⋮ On the prime graph of a finite group with unique nonabelian composition factor ⋮ Composition factors of the finite groups isospectral to simple classical groups ⋮ On finite groups isospectral to \(U_3(3)\) ⋮ On the nilpotency of the solvable radical of a finite group isospectral to a simple group ⋮ On recognition of alternating groups by prime graph ⋮ Finite groups isospectral to simple groups ⋮ On finite groups isospectral to simple classical groups. ⋮ Finite groups with arithmetic restrictions on maximal subgroups. ⋮ Recognizing M₁₀ by spectrum in the class of all groups ⋮ On finite groups isospectral to the simple group \(S_4(3)\) ⋮ On finite groups isospectral to the simple groups \(S_4(q)\) ⋮ Recognition of symplectic and orthogonal groups of small dimensions by spectrum ⋮ On groups having the prime graph as alternating and symmetric groups ⋮ Groups critical with respect to the spectra of alternating and sporadic groups. ⋮ Recognizability of symmetric groups by spectrum.

Cites Work

• Nilpotent groups and their automorphisms
• Finite groups whose element orders are consecutive integers
• An Adjacency Criterion for the Prime Graph of a Finite Simple Group
• A New Characterization ofA₂₂by Its Spectrum
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