Finite-dimensional pseudofinite groups of small dimension, without CFSG

Ulla KarhumäkiAGL, Frank Olaf WagnerAGL
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引用次数: 0

Abstract

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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无 CFSG 的小维度有限伪无限群
众所周知,任何单假无限群 G 都与假无限域上的(扭曲)切瓦利群同构。这一著名的结果主要源于威尔逊在 1995 年的工作,并在很大程度上依赖于有限简单群(CFSG)的分类。我们描述了当维度为细维度、加维度和 \<4 时的伪有限维群,并特别证明了 G 与 PSL(2,F) 的同构分类与 CFSG 无关。
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