Abstract
Let G be a finite group and N a normal subgroup of G. We determine the structure of N when the graph \(\Gamma _{G}(N)\), which is the graph associated to the conjugacy classes of G contained in N, has no triangles and when the graph consists in exactly one triangle.
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Acknowledgments
The results in this paper are part of the third author’s Ph.D. thesis at the University Jaume I of Castellón. The research of the first and second authors is supported by the Valencian Government, Proyecto PROMETEOII/2015/011. The first and the third authors are also partially supported by Universitat Jaume I, Grant P11B2015-77.
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Communicated by A. Constantin.
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Beltrán, A., Felipe, M.J. & Melchor, C. Triangles in the graph of conjugacy classes of normal subgroups. Monatsh Math 182, 5–21 (2017). https://doi.org/10.1007/s00605-015-0866-9
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DOI: https://doi.org/10.1007/s00605-015-0866-9