Character degrees in blocks and defect groups

Article Mathematics

Principal blocks with 5 irreducible characters

Noelia Rizo et al.

Summary: This study demonstrates that if the principal p-block of a finite group contains 5 irreducible characters, then the order of a Sylow p-subgroup can only be 5, 7, or isomorphic to a non-abelian 2-group of order 8.

JOURNAL OF ALGEBRA (2021)

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Article Mathematics

CHARACTERS AND GENERATION OF SYLOW 2-SUBGROUPS

Gabriel Navarro et al.

Summary: The character table of a finite group G can determine if a Sylow 2-subgroup of G is generated by 2 elements, with reference to the Galois action on characters. The proof of this result relies on the Classification of Finite Simple Groups and gives new support for the elusive Alperin-McKay-Navarro conjecture.

REPRESENTATION THEORY (2021)

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Article Mathematics

Brauer's Height Zero Conjecture for principal blocks

Gunter Malle et al.

Summary: In the case of principal blocks, we have proven the other half of Brauer's Height Zero Conjecture.

JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK (2021)

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Article Mathematics

Degrees of characters in the principal block

J. Miquel Martinez

Summary: In the study of finite groups, it was proven that if the set of character degrees in the principal p-block of G is at most 2, then G is p-solvable with a metabelian normal Sylow p-subgroup in G/O-p' (G). However, the question of whether defect groups are metabelian when an arbitrary p-block has two degrees remains unresolved.

JOURNAL OF ALGEBRA (2021)

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Article Mathematics, Applied