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We denote by [Formula: see text] the set of irreducible complex characters of G whose degrees are linear or divisible by p, and we write [Formula: see text] to denote the ratio of the sum of squares of irreducible character degrees in [Formula: see text] to the sum of irreducible character degrees in [Formula: see text]. The It\u00f4\u2013Michler Theorem on character degrees states that [Formula: see text] if and only if G has a normal abelian Sylow p-subgroup. We generalize this theorem as follows: if [Formula: see text], then G has a normal Sylow p-subgroup. <\/jats:p>","DOI":"10.1142\/s0218196724500164","type":"journal-article","created":{"date-parts":[[2024,4,5]],"date-time":"2024-04-05T15:07:17Z","timestamp":1712329637000},"page":"425-437","source":"Crossref","is-referenced-by-count":0,"title":["<i>p<\/i>-Singular characters and normal Sylow <i>p<\/i>-subgroups"],"prefix":"10.1142","volume":"34","author":[{"given":"Weijun","family":"Liu","sequence":"first","affiliation":[{"name":"College of General Education, Guangdong University of Science and Technology, Dongguan, Guangdong 523083, P. R. China"},{"name":"School of Mathematics and Statistics, HNP\u2013LAMA, Central South University, Changsha, Hunan 410083, P. R. 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