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PROBLEMS ON BRAUER CHARACTERS.

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Τίτλος: PROBLEMS ON BRAUER CHARACTERS.
Συγγραφείς: LIU, YANJUN1 liuyanjun@pku.edu.cn, WILLEMS, WOLFGANG2 wolfgang.willems@ovgu.de, ZHANG, JIPING3 jzhang@pku.edu.cn
Πηγή: International Journal of Group Theory. Dec2026, Vol. 15 Issue 4, p179-192. 14p.
Θεματικοί όροι: *Solvable groups, *Representations of groups (Algebra)
Περίληψη: In this paper we focus on problems of irreducible p-Brauer characters and state conjectures based on many examples which we computed. Many of the asked questions hold true for p-solvable groups, but their answers in general seem to require a much deeper understanding than we have at the moment. The questions are dealing with degrees, Hilbert divisors, divisibility, height-zero irreducible Brauer characters, number of irreducible Brauer characters in a p-block, and Cartan invariants. For instance, one of the main conjectures states that an irreducible Brauer character has Hilbert divisor 1 if and only if the character lies in a p-block of defect zero. This is true for p-solvable groups since in this case there is a relation between Hilbert divisors and vertices. However, even for a p-block of a non-p-solvable group containing only two irreducible Brauer characters we do not have an idea how to attack the problem. We hope that the conjectures and questions which we state in this paper will inspire further research. [ABSTRACT FROM AUTHOR]
Βάση Δεδομένων: Academic Search Index
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  Data: PROBLEMS ON BRAUER CHARACTERS.
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  Data: <searchLink fieldCode="AR" term="%22LIU%2C+YANJUN%22">LIU, YANJUN</searchLink><relatesTo>1</relatesTo><i> liuyanjun@pku.edu.cn</i><br /><searchLink fieldCode="AR" term="%22WILLEMS%2C+WOLFGANG%22">WILLEMS, WOLFGANG</searchLink><relatesTo>2</relatesTo><i> wolfgang.willems@ovgu.de</i><br /><searchLink fieldCode="AR" term="%22ZHANG%2C+JIPING%22">ZHANG, JIPING</searchLink><relatesTo>3</relatesTo><i> jzhang@pku.edu.cn</i>
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  Data: <searchLink fieldCode="JN" term="%22International+Journal+of+Group+Theory%22">International Journal of Group Theory</searchLink>. Dec2026, Vol. 15 Issue 4, p179-192. 14p.
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  Label: Abstract
  Group: Ab
  Data: In this paper we focus on problems of irreducible p-Brauer characters and state conjectures based on many examples which we computed. Many of the asked questions hold true for p-solvable groups, but their answers in general seem to require a much deeper understanding than we have at the moment. The questions are dealing with degrees, Hilbert divisors, divisibility, height-zero irreducible Brauer characters, number of irreducible Brauer characters in a p-block, and Cartan invariants. For instance, one of the main conjectures states that an irreducible Brauer character has Hilbert divisor 1 if and only if the character lies in a p-block of defect zero. This is true for p-solvable groups since in this case there is a relation between Hilbert divisors and vertices. However, even for a p-block of a non-p-solvable group containing only two irreducible Brauer characters we do not have an idea how to attack the problem. We hope that the conjectures and questions which we state in this paper will inspire further research. [ABSTRACT FROM AUTHOR]
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      – Type: doi
        Value: 10.22108/ijgt.2025.147244.1995
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      – Code: eng
        Text: English
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        PageCount: 14
        StartPage: 179
    Subjects:
      – SubjectFull: Solvable groups
        Type: general
      – SubjectFull: Representations of groups (Algebra)
        Type: general
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              M: 12
              Text: Dec2026
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              Y: 2026
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