Research output: Contribution to journal › Article

Journal | J. Reine Angew. Math. |
---|---|

Date | Published - Aug 2008 |

Issue number | 621 |

Volume | 621 |

Number of pages | 21 |

Pages (from-to) | 213-235 |

Original language | English |

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.

- Algebra

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