@article{53bc9a2add8442aaab7db02cbced8087,
title = "Abelian sylow subgroups in a finite group",
abstract = "Let p ≠ 3, 5 be a prime. We prove that Sylow p-subgroups of a finite group G are abelian if and only if the class sizes of the p-elements of G are all coprime to p. This gives a solution to a problem posed by R. Brauer in 1956 (for p ≠ 3, 5).",
keywords = "Abelian Sylow subgroups, Primary, Secondary",
author = "Gabriel Navarro and Tiep, {Pham Huu}",
note = "Funding Information: ✩ The authors are grateful to the referee for helpful comments on the paper. ✩✩ The research of the first author is supported by the Prometeo/Generalitat Valenciana, Proyectos MTM2010-15296. The second author gratefully acknowledges the support of the NSF (grants DMS-0901241 and DMS-1201374). * Corresponding author. E-mail addresses: gabriel.navarro@uv.es (G. Navarro), tiep@math.arizona.edu (P.H. Tiep).",
year = "2014",
month = jan,
day = "15",
doi = "10.1016/j.jalgebra.2013.04.007",
language = "English (US)",
volume = "398",
pages = "519--526",
journal = "Journal of Algebra",
issn = "0021-8693",
publisher = "Academic Press Inc.",
}