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- Title
A lower bound for the number of odd-degree representations of a finite group.
- Authors
Hung, Nguyen Ngoc; Keller, Thomas Michael; Yang, Yong
- Abstract
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.
- Publication
Mathematische Zeitschrift, 2021, Vol 298, Issue 3/4, p1559
- ISSN
0025-5874
- Publication type
Article
- DOI
10.1007/s00209-020-02660-z