Normal Sylow subgroups and monomial Brauer characters

Xiaoyou CHEN; Long MIAO

doi:10.1007/s11464-021-0970-1

Front. Math. China ›› 2022, Vol. 17 ›› Issue (4) : 567 -570. DOI: 10.1007/s11464-021-0970-1

RESEARCH ARTICLE

Normal Sylow subgroups and monomial Brauer characters

Xiaoyou CHEN ¹
, Long MIAO ²^,³^,^†

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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).

Keywords

Solvable group / monomial Brauer character / Sylow subgroup

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Xiaoyou CHEN, Long MIAO. Normal Sylow subgroups and monomial Brauer characters. Front. Math. China, 2022, 17(4): 567-570 DOI:10.1007/s11464-021-0970-1

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References

Publishing order | Descend order by publishing year | Descend order by cited within

[1]	Chen X Y , Lewis M L . Itô’s theorem and monomial Brauer characters. Bull Aust Math Soc, 2017, 96: 426- 428

[2]	Chen X Y , Lewis M L . Squares of degrees of Brauer characters and monomial Brauer characters. Bull Aust Math Soc, 2019, 100: 58- 60

[3]	Isaacs I M . Character Theory of Finite Groups. New York: Academic Press, 1976

[4]	Manz O , Wolf T R . Representations of Solvable Groups. London Math Soc Lecture Note Ser, Vol 185. Cambridge: Cambridge Univ Press, 1993

[5]	Navarro G . Characters and Blocks of Finite Groups. London Math Soc Lecture Note Ser, Vol 250. Cambridge: Cambridge Univ Press, 1998

[6]	Pang L , Lu J . Finite groups and degrees of irreducible monomial characters. J Algebra Appl, 2016, 15: 1650073 (4 pp)

[7]	Tong-Viet H P . Brauer characters and normal Sylow p-subgroups. J Algebra, 2018, 503: 265–276; Corrigendum to “Brauer characters and normal Sylow p-subgroups”. J Algebra, 2018, 505: 597- 598