@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.",

}