A note on the normal subgroup lattice of ultraproducts of finite\n quasisimple groups

2017/09/19 by Jakob Schneider, Andreas Thom, Schneider, Jakob +1
Mathematics · #Advanced Algebra and Geometry #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.1709.06286

openalex publication_date 2017/09/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In [A. Stolz and A. Thom, On the lattice of normal subgroups in ultraproducts\nof compact simple groups, PLMS 108(1), 2014] it was stated that the lattice of\nnormal subgroups of an ultraproduct of finite simple groups is always linearly\nordered. This is false in this form in most cases for classical groups of Lie\ntype. We correct the statement and point out a version of 'relative' bounded\ngeneration results for classical quasisimple groups and its implications on the\nstructure of the lattice of normal subgroups of an ultraproduct of quasisimple\ngroups.\n

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• The Ultraproducts of Quasirandom Groups
• Almost-minimal nonuniform lattices of higher rank
• Commensurators of normal subgroups of lattices
• Metric ultraproducts of finite simple groups
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