On a question of Külshammer for representations of finite groups in reductive groups Article Swipe

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Michael Bate , Benjamin Martin , Gerhard Röhrle ·

YOU? · · 2015 · Open Access · · DOI: https://doi.org/10.48550/arxiv.1505.00377

Let $G$ be a simple algebraic group of type $G_2$ over an algebraically closed field of characteristic $2$. We give an example of a finite group $Γ$ with Sylow $2$-subgroup $Γ_2$ and an infinite family of pairwise non-conjugate homomorphisms $ρ\colon Γ\rightarrow G$ whose restrictions to $Γ_2$ are all conjugate. This answers a question of Burkhard Külshammer from 1995. We also give an action of $Γ$ on a connected unipotent group $V$ such that the map of 1-cohomologies ${\rm H}^1(Γ,V)\rightarrow {\rm H}^1(Γ_p,V)$ induced by restriction of 1-cocycles has an infinite fibre.

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Unipotent Algebraically closed field Mathematics Algebraic group Homomorphism Sylow theorems Combinatorics Reductive group Conjugate Complement (music) Finite group Group (periodic table) Pure mathematics Algebraic number Physics Group theory Mathematical analysis Gene Complementation Phenotype Chemistry Biochemistry Quantum mechanics

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Type: preprint
Language: en
Landing Page: https://orcid.org/0000-0002-6513-2405>,
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Cited By: 1
References: 11
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DOI: https://doi.org/10.48550/arxiv.1505.00377

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Title: On a question of Külshammer for representations of finite groups in reductive groups

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Language: en

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Publication year: 2015

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Publication date: 2015-05-02

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Authors: Michael Bate, Benjamin Martin, Gerhard Röhrle

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Concepts: Unipotent, Algebraically closed field, Mathematics, Algebraic group, Homomorphism, Sylow theorems, Combinatorics, Reductive group, Conjugate, Complement (music), Finite group, Group (periodic table), Pure mathematics, Algebraic number, Physics, Group theory, Mathematical analysis, Gene, Complementation, Phenotype, Chemistry, Biochemistry, Quantum mechanics

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Cited by: 1

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abstract_inverted_index.H}^1(Γ,V)\rightarrow	78
cited_by_percentile_year
countries_distinct_count	0
institutions_distinct_count	3
citation_normalized_percentile