A characterization of the prime graphs of solvable groups.

DOI10.1016/j.jalgebra.2014.08.040zbMath1331.20029arXiv1305.2368OpenAlexW2963851574MaRDI QIDQ492997

Benjamin Strasser, Alexander Gruber, Mark L. Lewis, Thomas Michael Keller, Keeley Naughton

Publication date: 11 September 2015

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1305.2368

zbMATH Keywords

finite groupsFrobenius groupstriangle-free graphssolvable groupsprime graphssets of elements orders3-colorable graphs

Mathematics Subject Classification ID

Finite solvable groups, theory of formations, Schunck classes, Fitting classes, (pi)-length, ranks (20D10) Sylow subgroups, Sylow properties, (pi)-groups, (pi)-structure (20D20) Arithmetic and combinatorial problems involving abstract finite groups (20D60) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Coloring of graphs and hypergraphs (05C15)

Related Items (18)

Finite almost simple groups whose Gruenberg-Kegel graphs coincide with Gruenberg-Kegel graphs of solvable groups ⋮ Finite groups with given properties of their prime graphs ⋮ Criterion of unrecognizability of a finite group by its Gruenberg-Kegel graph ⋮ Finite groups whose prime graphs do not contain triangles. I ⋮ A new characterization of simple \(K_5\)-groups of type \(L_3(p)\) ⋮ The Gruenberg-Kegel graph of finite solvable rational groups ⋮ A classification of the prime graphs of pseudo-solvable groups ⋮ Gruenberg-Kegel graphs: cut groups, rational groups and the prime graph question ⋮ The prime graphs of groups with arithmetically small composition factors ⋮ The adjacency spectra of some families of minimally connected prime graphs ⋮ Simple groups whose Gruenberg-Kegel graph or solvable graph is split ⋮ Finite groups with prime graphs of diameter 5 ⋮ A combinatorial characterization of finite groups of prime exponent ⋮ The prime graphs of some classes of finite groups ⋮ On the Hawkes graphs of finite groups ⋮ The prime graph on class sizes of a finite group has a bipartite complement ⋮ Inverse graphs associated with finite groups ⋮ On finite non-solvable groups whose Gruenberg-Kegel graphs are isomorphic to the paw

Cites Work

• Finite groups with a five-component prime graph.
• On finite tetraprimary groups.
• On finite groups with disconnected prime graph.
• Prime graph components of finite groups
• Three short proofs in graph theory
• Character theory of finite groups
• Solvable groups with a small number of prime divisors in the element orders
• A linear bound for \(\rho(n)\)
• Groups and Rings Having Automorphisms without Non-Trivial Fixed Elements
• An Adjacency Criterion for the Prime Graph of a Finite Simple Group
• Recognizing Finite Groups Through Order and Degree Pattern
• The diameter of the prime graph of a finite group
• Combinatorial Relations and Chromatic Graphs
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