By the same authors

Complete Reducibility and Commuting Subgroups

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Complete Reducibility and Commuting Subgroups. / Bate, Michael Edward; Martin, Benjamin; Roehrle, Gerhard.

In: J. Reine Angew. Math., Vol. 621, No. 621, 08.2008, p. 213-235.

Research output: Contribution to journalArticle

Harvard

Bate, ME, Martin, B & Roehrle, G 2008, 'Complete Reducibility and Commuting Subgroups', J. Reine Angew. Math., vol. 621, no. 621, pp. 213-235.

APA

Bate, M. E., Martin, B., & Roehrle, G. (2008). Complete Reducibility and Commuting Subgroups. J. Reine Angew. Math., 621(621), 213-235.

Vancouver

Bate ME, Martin B, Roehrle G. Complete Reducibility and Commuting Subgroups. J. Reine Angew. Math. 2008 Aug;621(621):213-235.

Author

Bate, Michael Edward ; Martin, Benjamin ; Roehrle, Gerhard. / Complete Reducibility and Commuting Subgroups. In: J. Reine Angew. Math. 2008 ; Vol. 621, No. 621. pp. 213-235.

Bibtex - Download

@article{14615afdcf8b4352a201209cde93b8d4,
title = "Complete Reducibility and Commuting Subgroups",
abstract = "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.",
keywords = "Algebra",
author = "Bate, {Michael Edward} and Benjamin Martin and Gerhard Roehrle",
year = "2008",
month = "8",
language = "English",
volume = "621",
pages = "213--235",
journal = "J. Reine Angew. Math.",
number = "621",

}

RIS (suitable for import to EndNote) - Download

TY - JOUR

T1 - Complete Reducibility and Commuting Subgroups

AU - Bate, Michael Edward

AU - Martin, Benjamin

AU - Roehrle, Gerhard

PY - 2008/8

Y1 - 2008/8

N2 - 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.

AB - 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.

KW - Algebra

UR - http://www.scopus.com/inward/record.url?scp=46649090513&partnerID=8YFLogxK

M3 - Article

VL - 621

SP - 213

EP - 235

JO - J. Reine Angew. Math.

JF - J. Reine Angew. Math.

IS - 621

ER -