Research output: Contribution to journal › Article

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

Research output: Contribution to journal › Article

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

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

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

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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.",

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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 -