Hilbert divisors and degrees of irreducible Brauer characters
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Chaida Xu
and
Yuanyang Zhou
Abstract
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 𝜙 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.
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Communicated by: Britta Spaeth
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Articles in the same Issue
- Frontmatter
- On the kernel of actions on asymptotic cones
- CAT(0) cube complexes and asymptotically rigid mapping class groups
- Iwip endomorphisms of free groups and fixed points of graph selfmaps
- Space of orders with finite Cantor–Bendixson rank
- Lifting subgroups of PSL2 to SL2 over local fields
- Regular 3-polytopes of order 2𝑛𝑝
- On the number of tuples of group elements satisfying a first-order formula
- Exponent-critical groups
- On soluble groups in which commutators have prime power order
- A character theoretic criterion for Fitting height
- Hilbert divisors and degrees of irreducible Brauer characters
- Character triples and relative defect zero characters
Articles in the same Issue
- Frontmatter
- On the kernel of actions on asymptotic cones
- CAT(0) cube complexes and asymptotically rigid mapping class groups
- Iwip endomorphisms of free groups and fixed points of graph selfmaps
- Space of orders with finite Cantor–Bendixson rank
- Lifting subgroups of PSL2 to SL2 over local fields
- Regular 3-polytopes of order 2𝑛𝑝
- On the number of tuples of group elements satisfying a first-order formula
- Exponent-critical groups
- On soluble groups in which commutators have prime power order
- A character theoretic criterion for Fitting height
- Hilbert divisors and degrees of irreducible Brauer characters
- Character triples and relative defect zero characters
