论文标题
有限组的奇数表示数量的下限
A lower bound for the number of odd-degree representations of a finite group
论文作者
论文摘要
令$ g $为有限的组，$ p $ a sylow $ 2 $ -subgroup $ g $。对于$ g $的奇数不可约合的复杂表示数，就$ p $的$ g $而言，我们获得了渐近和明确的界限。为此，一方面，我们利用了Malle和Späth的Prime 2的最新证明，另一方面，我们证明了一个奇数组的半级产品的班级数量的下限，该类别是Abelian $ 2 $ 2的奇数组。
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.
