赋值对与可解群的几何

每对非共轭极大子群之积构成的有限群是可解群

Finite groups that are the product of every pair of non-conjugate maximal subgroups are soluble

该研究证明每对非共轭极大子群之积构成的有限群必可解，否定解决了Kourovka笔记的问题10.34，通过可除性准则及GAP验证消除一般情形的基S^k障碍。

Valuations, completions, and hyperbolic actions of metabelian groups

Actions on hyperbolic metric spaces are an important tool for studying groups, and so it is natural, but difficult, to attempt to classify all such actions of a fixed group. In this paper, we build strong connections between hyperbolic geometry and commutative algebra in order to classify the cobounded hyperbolic actions of numerous metabelian groups up to a coarse equivalence. In particular, we turn this classification problem into the problems of classifying ideals in the completions of certain rings and calculating invariant subspaces of matrices. We use this framework to classify the cobou…