@article{e953c0fc900e49bda44da5a0b87ce1ab,

title = "The average character degree and an improvement of the It{\^o}-Michler theorem",

abstract = "The classical It{\^o}-Michler theorem states that the degree of every ordinary irreducible character of a finite group G is coprime to a prime p if and only if the Sylow p-subgroups of G are abelian and normal. In an earlier paper [8], we used the notion of average character degree to prove an improvement of this theorem for the prime p=2. In this follow-up paper, we obtain a full improvement for all primes.",

keywords = "Character degrees, Finite groups, It{\^o}-Michler theorem, Normal subgroups, Simple groups, Sylow subgroups",

author = "Hung, {Nguyen Ngoc} and Tiep, {Pham Huu}",

note = "Funding Information: The second author gratefully acknowledges the support of the NSF (grant DMS-1840702 ) and the Joshua Barlaz Chair in Mathematics. The paper is partially based upon work supported by the NSF under grant DMS-1440140 while the authors were in residence at MSRI (Berkeley, CA), during the Spring 2018 semester. We thank the Institute for the hospitality and support. We also thank Jay Taylor for interesting discussion on the extendibility property of unipotent characters of finite groups of Lie type. The authors are grateful to the referee for insightful comments on the paper. Publisher Copyright: {\textcopyright} 2020",

year = "2020",

month = may,

day = "15",

doi = "10.1016/j.jalgebra.2019.12.022",

language = "English (US)",

volume = "550",

pages = "86--107",

journal = "Journal of Algebra",

issn = "0021-8693",

publisher = "Academic Press Inc.",

}