Normal Sylow subgroups and monomial Brauer characters |
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| Authors: | Xiaoyou CHEN Long MIAO |
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| Affiliation: | 1. School of Sciences, Henan University of Technology, Zhengzhou 450001, China2. College of Science, Hohai University, Nanjing 210098, China3. School of Mathematical Sciences, Yangzhou University, Yangzhou 225002, China |
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| Abstract: | Let G be a finite group, p be a prime divisor of |G|, and P be a Sylow p-subgroup of G. We prove that P is normal in a solvable group G if |G : ker φ|p' = φ(1)p' for every nonlinear irreducible monomial p-Brauer character φ of G, where ker φ is the kernel of φ and φ(1)p' is the p'-part of φ(1). |
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| Keywords: | Solvable group monomial Brauer character Sylow subgroup |
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