Curve Selection Lemma for semianalytic sets and conjugacy classes of finite order in Lie groups

Conjugacy problem in groups with quadratic Dehn function

We construct a finitely presented group with quadratic Dehn function and undecidable conjugacy problem. This solves E. Rips' problem formulated in 1992. v2: misprints corrected. v3: lemmas 4.7, 4.10 corrected, more misprints fixed.

论 Whitehead 的割点引理

On Whitehead's cut vertex lemma

本文将 Whitehead 割点引理从自由群元素推广到树上余紧作用群中的元素共轭类及凸余紧子群，并给出证明。

On the Conjugacy Classes in the orthogonal and symplectic groups over algebraically closed fields

Let $\F$ be an algebraically closed field. Let $\V$ be a vector space equipped with a non-degenerate symmetric or symplectic bilinear form $B$ over $\F$. Suppose the characteristic of $\F$ is \emph{large}, i.e. either zero or greater than the dimension of $\V$. Let $I(\V, B)$ denote the group of isometries. Using the Jacobson-Morozov lemma we give a new and simple proof of the fact that two elements in $I(\V,B)$ are conjugate if and only if they have the same elementary divisors.

超可解补群关于阿贝尔基底的共轭条件及非互素作用的不动点结果

Conjugacy conditions for supersoluble complements of an abelian base and a fixed point result for non-coprime actions

本文研究了有限分裂扩张中阿贝尔基底的超可解补群的共轭条件，证明了基于 Sylow $p$-子群共轭性的充要条件，并放宽了 Higman 的限制，最后得到了一个类似 Glauberman 引理的非互素作用不动点结果。

Construction of 2-local finite groups of a type studied by Solomon and Benson: Correction

We correct an error in Lemma 3.1 of my paper coauthored with Ran Levi on the Benson-Solomon fusion systems, and show that the change does not affect any of the other results in that paper. More precisely, as pointed out to us by Justin Lynd, there are two conjugacy classes of elementary abelian subgroups of rank $3$ in each of the fusion systems $\cal{F}_{\rm Sol}(q)$, and not only one as claimed in our paper.

交错群的二元作用

The binary actions of alternating groups

本文通过定义共轭类上的新图并建立二元作用与图连通性之间的引理，完整分类了交错群 A_n（n≥5）的所有二元作用。