Abstract
Let G be a finite solvable group and \(\pi (G)\) the set of primes that divide |G|. If, for every \(g\in G \setminus Z(G)\), we have \(|\pi \big (C_{G}(g) \big )| \le \kappa \), then we prove that \(|\pi (G)| \le 2\cdot \kappa \). We will then present some consequences of this result.
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Jabara, E. Centralizers in finite solvable groups. Arch. Math. 121, 225–230 (2023). https://doi.org/10.1007/s00013-023-01903-9
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DOI: https://doi.org/10.1007/s00013-023-01903-9