Permutation presentations of modules over finite groups

Takeshi Katsura

doi:10.1016/j.jalgebra.2008.01.023

Permutation presentations of modules over finite groups

Takeshi Katsura

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

1 Citation (Scopus)

Abstract

We introduce a notion of permutation presentations of modules over finite groups, and completely determine finite groups over which every module has a permutation presentation. To get this result, we prove that every coflasque module over a cyclic p-group is permutation projective.

Original language	English
Pages (from-to)	3653-3665
Number of pages	13
Journal	Journal of Algebra
Volume	319
Issue number	9
DOIs	https://doi.org/10.1016/j.jalgebra.2008.01.023
Publication status	Published - 2008 May 1
Externally published	Yes

Keywords

Coflasque module
Finite group
Group cohomology
Module
Permutation module
Permutation presentation
Sylow group

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jalgebra.2008.01.023

Cite this

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title = "Permutation presentations of modules over finite groups",

abstract = "We introduce a notion of permutation presentations of modules over finite groups, and completely determine finite groups over which every module has a permutation presentation. To get this result, we prove that every coflasque module over a cyclic p-group is permutation projective.",

keywords = "Coflasque module, Finite group, Group cohomology, Module, Permutation module, Permutation presentation, Sylow group",

author = "Takeshi Katsura",

year = "2008",

month = may,

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doi = "10.1016/j.jalgebra.2008.01.023",

language = "English",

volume = "319",

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journal = "Journal of Algebra",

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AU - Katsura, Takeshi

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N2 - We introduce a notion of permutation presentations of modules over finite groups, and completely determine finite groups over which every module has a permutation presentation. To get this result, we prove that every coflasque module over a cyclic p-group is permutation projective.

AB - We introduce a notion of permutation presentations of modules over finite groups, and completely determine finite groups over which every module has a permutation presentation. To get this result, we prove that every coflasque module over a cyclic p-group is permutation projective.

KW - Coflasque module

KW - Finite group

KW - Group cohomology

KW - Module

KW - Permutation module

KW - Permutation presentation

KW - Sylow group

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DO - 10.1016/j.jalgebra.2008.01.023

M3 - Article

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SN - 0021-8693

VL - 319

SP - 3653

EP - 3665

JO - Journal of Algebra

JF - Journal of Algebra

IS - 9

ER -

Permutation presentations of modules over finite groups

Abstract

Keywords

ASJC Scopus subject areas

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