Abstract
Let \(G\) be a finite \(p\)-solvable group for some prime \(p\) and suppose that the set of \(p\)-regular conjugacy class sizes is \(\{1, m, mn\}\) with \((m, n)=1\) and \(m\) coprime to \(p\). We show that \(m=q^b\) for some prime \(q\) and we describe the structure of the \(p\)-complements of \(G\).
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Acknowledgments
This research is supported by the Spanish Government, Proyecto MTM2010-19938-C03-02 and by the Valencian Government, Proyecto PROMETEO/2011/30. The first author is also supported by grant Fundació Caixa-Castelló P11B2010-47.
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Communicated by J. S. Wilson.
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Beltrán, A., Felipe, M.J. Structure of \(p\)-complements in groups with three \(p\)-regular class sizes. Monatsh Math 171, 157–167 (2013). https://doi.org/10.1007/s00605-012-0466-x
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DOI: https://doi.org/10.1007/s00605-012-0466-x