Complete Reducibility and Commuting Subgroups

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dc.creatorBate, M.
dc.creatorMartin, B. M. S.
dc.creatorRoehrle, G. E.
dc.date2006-09-15
dc.date2008-02-29
dc.date.accessioned2026-07-07T09:23:49Z
dc.date.available2026-07-07T09:23:49Z
dc.descriptionLet G be a reductive linear algebraic group over an algebraically closed field of characteristic p. We study J.-P. Serre's notion of G-complete reducibility for subgroups of G. In particular, for a subgroup H and a normal subgroup N of H, we look at the relationship between G-complete reducibility of N and of H, and show that these properties are equivalent if H/N is linearly reductive, generalizing a result of Serre. We also study the case when H = MN with M a G-completely reducible subgroup of G which normalizes N. We show that if G is connected, N and M are connected commuting G-completely reducible subgroups of G, and p is good for G, then H = MN is also G-completely reducible.
dc.description21 pages; to appear in J. Reine Angew. Math. final form
dc.identifierhttps://arxiv.org/abs/math/0609433
dc.identifierhttp://arxiv.org/abs/math/0609433
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/155877
dc.subjectGroup Theory
dc.subjectAlgebraic Geometry
dc.subject20G15, 14L24
dc.titleComplete Reducibility and Commuting Subgroups
dc.typetext

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