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On a graph associated to invariant conjugacy classes of finite groups |
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| Authors: | Antonio?Beltrán mailto:abeltran@mat.uji.es" title=" abeltran@mat.uji.es" itemprop=" email" data-track=" click" data-track-action=" Email author" data-track-label=" " >Email author |
| Affiliation: | (1) Departamento de Matemáticas, Universidad Jaume I, 12071 Castellón, Spain |
| Abstract: | LetA andG be finite groups of coprime orders such thatA acts by automorphisms onG. We define theA-invariant conjugacy class graph ofG to be the graph having as vertices the noncentralA-invariant conjugacy classes ofG, and two vertices are connected by an edge if their cardinalities are not coprime. We prove that when the graph is disconnected thenG is solvable. |
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