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arXiv · 2004.03091

A lower bound for the number of odd-degree representations of a finite group

Nguyen Ngoc Hung·Thomas Michael Keller·Yong Yang
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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 Sp\"{a}th, 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.

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Nguyen Ngoc Hung, Thomas Michael Keller, Yong Yang. 2020-04-07. A lower bound for the number of odd-degree representations of a finite group. https://arxiv.org/abs/2004.03091

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