On finite groups with disconnected prime graph.

DOI10.1134/S0081543813090149zbMath1307.20023OpenAlexW2124578059MaRDI QIDQ483212

M. R. Zinov'eva, Victor D. Mazurov

Publication date: 16 December 2014

Published in: Proceedings of the Steklov Institute of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0081543813090149

zbMATH Keywords

Frobenius groupsfinite simple groupsprime graphsrecognition by spectrasets of element ordersrecognizable groups2-Frobenius groups

Mathematics Subject Classification ID

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

Finite groups with given properties of their prime graphs ⋮ Criterion of unrecognizability of a finite group by its Gruenberg-Kegel graph ⋮ Finite almost simple groups with prime graphs all of whose connected components are cliques ⋮ On recognition of alternating groups by prime graph ⋮ Gruenberg-Kegel graphs: cut groups, rational groups and the prime graph question ⋮ A characterization of the prime graphs of solvable groups. ⋮ On quasirecognition by prime graph of the simple groups $A^{+}_{n}(p)$ and $A^{-}_{n}(p)$ ⋮ On the coincidence of Gruenberg-Kegel graphs of an almost simple group and a nonsolvable Frobenius group ⋮ Several quantitative characterizations of some specific groups ⋮ 2-Frobenius groups isospectral to the simple group \(U_3(3)\).

Cites Work

• Cocliques of maximal size in the prime graph of a finite simple group
• Prime graph components of finite groups
• Recognition of alternating groups of prime degree from their element orders
• On finite simple groups with the set of element orders as in a Frobenius group or a double Frobenius group.
• An Adjacency Criterion for the Prime Graph of a Finite Simple Group
• PRIME GRAPH COMPONENTS OF FINITE SIMPLE GROUPS
• Decomposition of the Augmentation Ideal and of the Relation Modules of a Finite Group
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