L. G. Kovács对置换群理论的研究

拟本原群与blow-up分解

Quasiprimitive groups and blow-up decompositions

L. G. Kovács是研究有限本原置换群在乘积作用下嵌入到圈积中的一个非常有用的工具。本文将Blow-up的概念推广到有限拟本原置换群，并利用它研究了有限拟本原群到圈积的嵌入。

含圈的本原置换群

Primitive permutation groups containing a cycle

对含圈的本原有限置换群进行了分类。其中，只有交替群和对称群包含至少固定三个点的循环。约旦和Marggraff对这一主题的贡献进行了简要讨论。

Real Constituents of Permutation Characters

We prove a broad generalization of a theorem of W. Burnside on real characters using permutation characters. Under a necessary hypothesis, We can give some control on multiplicities (a result that needs the Classification of Finite Simple Groups). Along the way, we also give a new characterization of the 2-closed finite groups using odd-order real elements of the group. All this can be seen as a contribution to Brauer's Problem 11. We also obtain similar results for 2-Brauer characters. We also classify finite primitive permutation groups in which every real element has a fixed point.

随机单纯复形排列中的余子稳定性

Cocycle stability in permutations of random simplicial complexes

本文通过研究随机二维Linial-Meshulam复形排列中的余子稳定性，提出了一种概率方法，证明在特定密度范围内存在非sofic的超几何群。

On base sizes for algebraic groups

Let $G$ be a permutation group on a set $Ω$. A subset of $Ω$ is a base for $G$ if its pointwise stabilizer is trivial; the base size of $G$ is the minimal cardinality of a base. In this paper we initiate the study of bases for algebraic groups defined over an algebraically closed field. In particular, we calculate the base size for all primitive actions of simple algebraic groups, obtaining the precise value in almost all cases. We also introduce and study two new base measures, which arise naturally in this setting. We give an application concerning the essential dimension of simple algebraic…