Isomorphism questions for metric ultraproducts of finite quasisimple\n groups

2019/11/11 by Jakob Schneider, Schneider, Jakob
Mathematics · #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.1911.04245

openalex publication_date 2019/11/11 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

New results on metric ultraproducts of finite simple groups are established.\nWe show that the isomorphism type of a simple metric ultraproduct of groups\nX_ni(q) (i\∈ I) for X\∈ rm PGL, rm PSp, rm\nPGO^(\ε), rm PGU (\ε=\±) along an ultrafilter\n\U on the index set I for which n_i\→_\U\∞\ndetermines the type X and the field size q up to the possible isomorphism\nof a metric ultraproduct of groups rm PSp_ni(q) and a metric\nultraproduct of groups rm PGO_ni^(\ε)(q). This extends\nresults of Thom and Wilson.\n

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