Orders of elements and zeros and heights of characters in a finite group

最小高度与具有两个特征标度的亏群

Minimal heights and defect groups with two character degrees

本文证明了当亏群具有两个特征标度时，主块中最小正高度等于亏群中最小正高度，从而推广了 Brauer 零高度猜想。

高度零特征标的值域

The Field of Values of the Height Zero Characters

本文研究有限群不可约 p-高度零特征标的值域，完整确定 p=2 的情形，并对奇素数提出猜想且归结为拟单群块问题。

Characters of positive height in blocks of finite quasi-simple groups

Eaton and Moretó proposed an extension of Brauer's famous height zero conjecture on blocks of finite groups to the case of non-abelian defect groups, which predicts the smallest non-zero height in such blocks in terms of local data. We show that their conjecture holds for principal blocks of quasi-simple groups, for all blocks of finite reductive groups in their defining characteristic, as well as for all covering groups of symmetric and alternating groups. For the proof, we determine the minimal non-trivial character degrees of Sylow $p$-subgroups of finite reductive groups in characteristic~…

高度零特征标的 $p$-有理性

The $p$-rationality of height-zero characters

本文提出并佐证一项全局—局部猜想：有限群中 $p$-高度零特征标的 $p$-有理性可由其亏群的正规化子刻画。

Height Zero Conjecture with Galois Automorphisms

We prove a strengthening of Brauer's height zero conjecture for principal 2-blocks with Galois automorphisms. This requires a new extension of the Itô--Michler theorem for the prime~2, again with Galois automorphisms. We close, this time for odd primes $p$, with a new characterisation of $p$-closed groups via the decomposition numbers of certain characters.

关于可解群块的零高度类型结果

A height-zero type result for blocks of solvable groups

本文研究了可解群中块的缺陷群性质，证明在特定条件下缺陷群为阿贝尔群，且对p=2或3时近似阿贝尔。