酉性（unital）的一个同构，以及经典群的一个同构

二阶广义六边形中的一个 unital，以及有限李型群之间的一个例外同构

A unital in the generalized hexagon of order two, and an exceptional isomorphism between finite groups of Lie type

本文在二阶域上的八元数代数中构造三阶 Hermitian unital 模型，以说明例外李型有限群与 Hermite 型半相似群之间的已知同构。

The Classification Problem for Simple Unital Finite Rank Dimension Groups

The Borel complexity of the isomorphism problem for finite-rank unital simple dimension groups increases with rank. This implies that the isomorphism problems for the corresponding classes of Bratteli diagrams and LDA-groups also increase with rank.

Isomorphism Invariants for Linear Quasigroups

For a unital ring $S$, an $S$-linear quasigroup is a unital $S$-module, with automorphisms $ρ$ and $λ$ giving a (nonassociative) multiplication $x\cdot y=x^ρ+y^λ$. If $S$ is the field of complex numbers, then ordinary characters provide a complete linear isomorphism invariant for finite-dimensional $S$-linear quasigroups. Over other rings, it is an open problem to determine tractably computable isomorphism invariants. The paper investigates this isomorphism problem for $\mathbb{Z}$-linear quasigroups. We consider the extent to which ordinary characters classify $\mathbb{Z}$-linear quasigroups …

模同构问题的几何方法：阶为64的群

Geometric approach to the modular isomorphism problem: groups of order 64

通过计算代数几何方法研究群的模同构问题，证明在特定条件下群的同构性与模代数同构性等价。

The isomorphism problem for group algebras: a criterion

Let $R$ be a finite unital commutative ring. We introduce a new class of finite groups, which we call hereditary groups over $R$. Our main result states that if $G$ is a hereditary group over $R$ then a unital algebra isomorphism between group algebras $RG \cong RH$ implies a group isomorphism $G \cong H$ for every finite group $H$. As application, we study the modular isomorphism problem, which is the isomorphism problem for finite $p$-groups over $R = \mathbb{F}_p$ where $\mathbb{F}_p$ is the field of $p$ elements. We prove that a finite $p$-group $G$ is a hereditary group over $\mathbb{F}_p…

由酉平移生成的Moufang集

Moufang sets generated by translations in unitals

本文研究带两个q阶平移群中心的q阶unital，证明其平移生成群在两点连块上诱导Moufang集，且该群为SL(2,F_q)、PSL(2,F_q)、Suzuki群或Ree群，在特殊块外半正则。