@article{33c60ded982242e1b529a65e6f9b986a,

title = "Abelian Sylow subgroups in a finite group, II",

abstract = "Let p 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, and, if p∈. {3, 5}, the degree of every irreducible character in the principal p-block of G is coprime to p. This gives a complete solution to a problem posed by R. Brauer in 1963.",

keywords = "Abelian Sylow subgroups",

author = "Gabriel Navarro and Ronald Solomon and Tiep, {Pham Huu}",

note = "Funding Information: The research of the first author is supported by the Prometeo/Generalitat Valenciana , Proyectos MTM2010-15296 . The research of the second author was supported by the Mathematical Research Institute of the Ohio State University, and by the NSA (grant H98230-13-1-0229 ). The third author gratefully acknowledges the support of the NSF (grant DMS-1201374 ) and the Simons Foundation Fellowship 305247 . Publisher Copyright: {\textcopyright} 2014 Elsevier Inc.",

year = "2015",

month = jan,

day = "1",

doi = "10.1016/j.jalgebra.2014.08.012",

language = "English (US)",

volume = "421",

pages = "3--11",

journal = "Journal of Algebra",

issn = "0021-8693",

publisher = "Academic Press Inc.",

}