A note on the normal subgroup lattice of ultraproducts of finite quasisimple groups
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- by Jakob Schneider and Andreas Thom PDF
- Proc. Amer. Math. Soc. 149 (2021), 1929-1942 Request permission
Abstract:
Abel Stolz and Andreas Thom [Proc. Lond. Math. Soc. 108 (2014), pp. 73–102] stated that the lattice of normal subgroups of an ultraproduct of finite simple groups is always linearly ordered. This is false in this form in most cases for classical groups of Lie type. We correct the statement in this case and point out a version of \enquote*relative bounded normal generation for classical quasisimple groups and its implications on the structure of the lattice of normal subgroups of an ultraproduct of such groups.References
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Additional Information
- Jakob Schneider
- Affiliation: TU Dresden, 01062 Dresden, Germany
- MR Author ID: 1249483
- Email: jakob.schneider@tu-dresden.de
- Andreas Thom
- Affiliation: TU Dresden, 01062 Dresden, Germany
- MR Author ID: 780176
- ORCID: 0000-0002-7245-2861
- Email: andreas.thom@tu-dresden.de
- Received by editor(s): November 19, 2019
- Received by editor(s) in revised form: August 31, 2020
- Published electronically: March 2, 2021
- Additional Notes: This research was supported by ERC Consolidator Grant No. 681207.
- Communicated by: Martin Liebeck
- © Copyright 2021 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 149 (2021), 1929-1942
- MSC (2020): Primary 20D06, 20F69
- DOI: https://doi.org/10.1090/proc/15385
- MathSciNet review: 4232187