Degrees of characters in the principal block

Let G be a finite group. We prove that if the set of degrees of characters in the principal p-block of G has size at most 2 then G is p-solvable, and G/Op′(G) has a metabelian normal Sylow p-subgroup. The general question of proving that if an arbitrary p-block has two degrees then their defect grou...

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Bibliographic Details
Published in:Journal of algebra 2021-08, Vol.579, p.195-209
Main Author: Martínez, J. Miquel
Format: Article
Language:English
Subjects:
Degrees of characters
Principal blocks
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Summary:Let G be a finite group. We prove that if the set of degrees of characters in the principal p-block of G has size at most 2 then G is p-solvable, and G/Op′(G) has a metabelian normal Sylow p-subgroup. The general question of proving that if an arbitrary p-block has two degrees then their defect groups are metabelian remains open.
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2021.03.026