On fully ramified Brauer characters

Gabriel Navarro; Britta Späth; Pham Huu Tiep

doi:10.1016/j.aim.2014.02.014

On fully ramified Brauer characters

Gabriel Navarro, Britta Späth, Pham Huu Tiep

Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

Let Z be a normal subgroup of a finite group, let p ≠ 5 be a prime and let λ ∈ IBr(Z) be an irreducible G-invariant p-Brauer character of Z. Suppose that ^λG = eφ for some φ ∈ IBr(G). Then G/Z is solvable. In other words, a twisted group algebra over an algebraically closed field of characteristic not 5 with a unique class of simple modules comes from a solvable group.

Original language	English (US)
Pages (from-to)	248-265
Number of pages	18
Journal	Advances in Mathematics
Volume	257
DOIs	https://doi.org/10.1016/j.aim.2014.02.014
State	Published - Jun 1 2014

Keywords

Brauer characters
Fully ramified characters
Group theory
Primary
Representation theory
Secondary

ASJC Scopus subject areas

General Mathematics

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10.1016/j.aim.2014.02.014

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title = "On fully ramified Brauer characters",

abstract = "Let Z be a normal subgroup of a finite group, let p ≠ 5 be a prime and let λ ∈ IBr(Z) be an irreducible G-invariant p-Brauer character of Z. Suppose that λG = eφ for some φ ∈ IBr(G). Then G/Z is solvable. In other words, a twisted group algebra over an algebraically closed field of characteristic not 5 with a unique class of simple modules comes from a solvable group.",

keywords = "Brauer characters, Fully ramified characters, Group theory, Primary, Representation theory, Secondary",

author = "Gabriel Navarro and Britta Sp{\"a}th and Tiep, {Pham Huu}",

note = "Funding Information: The research of the first author is partially supported by the Spanish Ministerio de Educaci{\'o}n y Ciencia proyecto MTM2010-15296 , and Prometeo/Generalitat Valenciana . The research of the second author has been supported by the Deutsche Forschungsgemeinschaft , SPP 1388 and the ERC Advanced Grant 291512 . The third author gratefully acknowledges the support of the NSF (Grants DMS-0901241 and DMS-1201374 ). ",

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doi = "10.1016/j.aim.2014.02.014",

language = "English (US)",

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T1 - On fully ramified Brauer characters

AU - Navarro, Gabriel

AU - Späth, Britta

AU - Tiep, Pham Huu

N1 - Funding Information: The research of the first author is partially supported by the Spanish Ministerio de Educación y Ciencia proyecto MTM2010-15296 , and Prometeo/Generalitat Valenciana . The research of the second author has been supported by the Deutsche Forschungsgemeinschaft , SPP 1388 and the ERC Advanced Grant 291512 . The third author gratefully acknowledges the support of the NSF (Grants DMS-0901241 and DMS-1201374 ).

PY - 2014/6/1

Y1 - 2014/6/1

N2 - Let Z be a normal subgroup of a finite group, let p ≠ 5 be a prime and let λ ∈ IBr(Z) be an irreducible G-invariant p-Brauer character of Z. Suppose that λG = eφ for some φ ∈ IBr(G). Then G/Z is solvable. In other words, a twisted group algebra over an algebraically closed field of characteristic not 5 with a unique class of simple modules comes from a solvable group.

AB - Let Z be a normal subgroup of a finite group, let p ≠ 5 be a prime and let λ ∈ IBr(Z) be an irreducible G-invariant p-Brauer character of Z. Suppose that λG = eφ for some φ ∈ IBr(G). Then G/Z is solvable. In other words, a twisted group algebra over an algebraically closed field of characteristic not 5 with a unique class of simple modules comes from a solvable group.

KW - Brauer characters

KW - Fully ramified characters

KW - Group theory

KW - Primary

KW - Representation theory

KW - Secondary

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DO - 10.1016/j.aim.2014.02.014

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VL - 257

SP - 248

EP - 265

JO - Advances in Mathematics

JF - Advances in Mathematics

ER -

On fully ramified Brauer characters

Abstract

Keywords

ASJC Scopus subject areas

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