Hilbert divisors and degrees of irreducible Brauer characters
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作者:
Xu, Chaida
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Wuhan Inst Technol, Sch Math & Phys, Wuhan, Peoples R ChinaWuhan Inst Technol, Sch Math & Phys, Wuhan, Peoples R China
Xu, Chaida
[1
]
Zhang, Kun
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Hubei Univ, Fac Math & Stat, Wuhan, Peoples R ChinaWuhan Inst Technol, Sch Math & Phys, Wuhan, Peoples R China
Zhang, Kun
[2
]
Zhou, Yuanyang
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机构:
Cent China Normal Univ, Sch Math & Stat, Wuhan, Peoples R China
Cent China Normal Univ, Key Lab Nonlinear Anal & Applicat, Wuhan, Peoples R ChinaWuhan Inst Technol, Sch Math & Phys, Wuhan, Peoples R China
Zhou, Yuanyang
[3
,4
]
机构:
[1] Wuhan Inst Technol, Sch Math & Phys, Wuhan, Peoples R China
[2] Hubei Univ, Fac Math & Stat, Wuhan, Peoples R China
[3] Cent China Normal Univ, Sch Math & Stat, Wuhan, Peoples R China
[4] Cent China Normal Univ, Key Lab Nonlinear Anal & Applicat, Wuhan, Peoples R China
In this paper, we prove that the Hilbert divisors of irreducible Brauer characters in 2-blocks with nontrivial abelian defect groups are strictly greater than 1. This confirms a conjecture of Liu and Willems in this case. The proof relates the conjecture with a problem of Feit, which asks if the p-part of the degree of an irreducible Brauer character phi of G is always less than the p-part of the order of G. We resolve Feit's problem positively for 2-blocks with abelian defect groups. But it is well known that the question has a negative answer for 2-blocks with non-abelian defect groups.