On the vanishing prime graph of solvable groups

DOI10.1515/JGT.2009.046zbMath1196.20029OpenAlexW2080463716MaRDI QIDQ3552303

Emanuele Pacifici, Lucia Sanus, Pablo Spiga, Silvio Dolfi

Publication date: 15 April 2010

Published in: Journal of Group Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/jgt.2009.046

zbMATH Keywords

finite solvable groupsirreducible complex charactersprime graphsvanishing elements

Mathematics Subject Classification ID

Ordinary representations and characters (20C15) Finite solvable groups, theory of formations, Schunck classes, Fitting classes, (pi)-length, ranks (20D10) Arithmetic and combinatorial problems involving abstract finite groups (20D60) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25)

Related Items (14)

Recognition of \(\mathrm{PSL}(2,2)^a)\) by the orders of vanishing elements ⋮ Groups whose vanishing elements are of odd order ⋮ Characterization of some finite simple groups by the set of orders of vanishing elements and order ⋮ A new characterization of Suzuki’s simple groups ⋮ The Isaacs-Navarro-Wolf conjecture for groups with one vanishing class size ⋮ Finite groups with some restriction on the vanishing set ⋮ On solvable groups with one vanishing class size ⋮ On the orders of vanishing elements of finite groups ⋮ Recognition of some finite simple groups by the orders of vanishing elements ⋮ Groups with vanishing class size \(p\) ⋮ Unnamed Item ⋮ Groups whose vanishing class sizes are prime powers ⋮ On the proportion of vanishing elements in finite groups ⋮ A new characterization of some finite simple groups.

Cites Work

• Prime graph components of finite groups
• On the character degree graph of solvable groups. I: Three primes
• Arithmetical conditions on the length of the conjugacy classes of a finite group
• Finite group elements where no irreducible character vanishes
• Finite groups whose irreducible characters vanish only on \(p\)-elements.
• On the orders of zeros of irreducible characters.
• The diameter of the prime graph of a finite group

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