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Characters, exponents and defects in p-solvable groups

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Abstract

Suppose that χ is an irreducible complex character in a Brauer p-block B of a finite p-solvable G group, where p ≥ 5 is a prime. If D is the defect group of B, then we prove that the exponent of D is less than or equal to (∣G∣/χ(1))p. Our proof depends on highly non-trivial properties of p-groups.

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Authors and Affiliations

  1. Departament de Matemàtiques, Universitat de València, 46100, Burjassot, València, Spain

    Alexander Moretó & Gabriel Navarro

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  1. Alexander Moretó
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  2. Gabriel Navarro
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Correspondence to Gabriel Navarro.

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Moretó, A., Navarro, G. Characters, exponents and defects in p-solvable groups. Isr. J. Math. 249, 553–576 (2022). https://doi.org/10.1007/s11856-022-2319-1

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  • DOI: https://doi.org/10.1007/s11856-022-2319-1

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