On the vanishing prime graph of finite groups

• Autores: Silvio Dolfi , Emanuele Pacifici , Lucía Sanus Vitoria , Pablo Spiga
• Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 82, Nº 1, 2010, págs. 167-183
• Idioma: inglés
• DOI: 10.1112/jlms/jdq021
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• Resumen

  • Let G be a finite group. An element g �¸ G is called a vanishing element of G if there exists an irreducible complex character �Ô of G such that �Ô(g) = 0. In this paper we study the vanishing prime graph �¡(G), whose vertices are the prime numbers dividing the orders of some vanishing element of G, and two distinct vertices p and q are adjacent if and only if G has a vanishing element of order divisible by pq. Among other things we prove that, similarly to what holds for the prime graph of G, the graph �¡(G) has at most six connected components.