Complete Reducibility and Commuting Subgroups

Michael Edward Bate, Benjamin Martin, Gerhard Roehrle

Research output: Contribution to journalArticlepeer-review


Let 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.
Original languageEnglish
Pages (from-to)213-235
Number of pages21
JournalJournal für die reine und angewandte Mathematik
Issue number621
Publication statusPublished - Aug 2008


  • Algebra

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