Let G be a finite group, and write cd(G) for the set of degrees of irreducible characters of G. We define I(G) to be the graph whose vertex set is cd(G)-{1}, and there is an edge between a and b if (a, b) > 1. We prove that if I(G) is a complete graph, then G is a solvable group. © 2006 American Mathematical Society.
Character degree graphs that are complete graphs / Bianchi M.; Chillag D.; Lewis M.L.; Pacifici E.. - In: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9939. - STAMPA. - 135:(2007), pp. 671-676. [10.1090/S0002-9939-06-08651-5]
Character degree graphs that are complete graphs
Pacifici E.
2007
Abstract
Let G be a finite group, and write cd(G) for the set of degrees of irreducible characters of G. We define I(G) to be the graph whose vertex set is cd(G)-{1}, and there is an edge between a and b if (a, b) > 1. We prove that if I(G) is a complete graph, then G is a solvable group. © 2006 American Mathematical Society.
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