Bate, MichaelBöhm, SörenLitterick, AlastairMartin, BenjaminRoehrle, Gerhard2025-04-032025-04-032025-06-02Bate, M, Böhm, S, Litterick, A, Martin, B & Roehrle, G 2025, 'G -complete reducibility and saturation', Pacific Journal of Mathematics, vol. 337, no. 1, pp. 1-24. https://doi.org/10.2140/pjm.2025.337.10030-8730ORCID: /0000-0002-6670-0857/work/190041062https://hdl.handle.net/2164/25254Acknowledgments: We are grateful to J-P. Serre for some suggestions on an earlier version of the manuscript. For the purpose of open access, the authors have applied a Creative Commons Attribution (CC BY) licence to any Author Accepted Manuscript version arising from this submission. Open Access made possible by participating institutions via Subscribe to Open.24268845463560engmath.RTmath.GR20G15, 14L24G -complete reducibilitysaturationfinite groups of Lie typeQA MathematicsQAJournal article10.2140/pjm.2025.337.13371