不依赖CFSG的小维度有限维伪有限群
Finite-dimensional pseudofinite groups of small dimension, without CFSG
AI总结：
该研究针对伪有限群分类依赖有限单群分类（CFSG）的问题，刻画了维度小于4的加法精细维有限维伪有限群，证明了3维单伪有限群同构于PSL(2,F)的结论无需依赖CFSG。
摘要：
已知任意单伪有限群G同构于伪有限域上的（扭）Chevalley群。这一著名结果主要源自Wilson1995年的工作，且严重依赖有限单群分类（CFSG）。由此可轻松推得G是具有加法精细维度的有限维群，尤其当dim(G)=3时，G同构于某伪有限域F上的PSL(2,F)。我们刻画了维度为精细、加法且小于4的伪有限有限维群，特别证明了G同构于PSL(2,F)的分类结论与CFSG无关。
英文摘要：
Any simple pseudofinite group G is known to be isomorphic to a (twisted) Chevalley group over a pseudofinite field. This celebrated result mostly follows from the work of Wilson in 1995 and heavily relies on the classification of finite simple groups (CFSG). It easily follows that G is finite-dimensional with additive and fine dimension and, in particular, that if dim(G)=3 then G is isomorphic to PSL(2,F) for some pseudofinite field F. We describe pseudofinite finite-dimensional groups when the dimension is fine, additive and \<4 and, in particular, show that the classification G isomorphic to PSL(2,F) is independent from CFSG.
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