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Let G be a finite group and P a Sylow 2-subgroup of G. We obtain both asymptotic and explicit bounds for the number of odd-degree irreducible complex representations of G in terms of the size of the abelianization of P. To do so, we, on one hand, make use of the recent proof of the McKay conjecture for the prime 2 by Malle and Späth, and, on the other hand, prove lower bounds for the class number of the semidirect product of an odd-order group acting on an abelian 2-group.
Mathematische Zeitschrift – Springer Journals
Published: Jan 5, 2021
Keywords: Finite groups; Odd-degree representations; Characters; Coprime action; Primary 20C15; 20D10; 20D05
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