Periodicity of Adams operations on the Green ring of a finite group

R. M. Bryant; Marianne Johnson

doi:10.1016/j.jpaa.2010.07.005

Periodicity of Adams operations on the Green ring of a finite group

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Abstract

The Adams operations ψΛn and ψsn on the Green ring of a group G over a field K arise from the study of the exterior powers and symmetric powers of KG-modules. When G is finite and K has prime characteristic p we show that ψΛn and ψsn are periodic in n if and only if the Sylow p-subgroups of G are cyclic. In the case where G is a cyclic p-group we find the minimum periods and use recent work of Symonds to express ψSn in terms of ψΛn. © 2010 Elsevier B.V.

Original language	English
Pages (from-to)	989-1002
Number of pages	13
Journal	Journal of Pure and Applied Algebra
Volume	215
Issue number	5
DOIs	https://doi.org/10.1016/j.jpaa.2010.07.005
Publication status	Published - May 2011

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title = "Periodicity of Adams operations on the Green ring of a finite group",

abstract = "The Adams operations ψΛn and ψsn on the Green ring of a group G over a field K arise from the study of the exterior powers and symmetric powers of KG-modules. When G is finite and K has prime characteristic p we show that ψΛn and ψsn are periodic in n if and only if the Sylow p-subgroups of G are cyclic. In the case where G is a cyclic p-group we find the minimum periods and use recent work of Symonds to express ψSn in terms of ψΛn. {\textcopyright} 2010 Elsevier B.V.",

author = "Bryant, {R. M.} and Marianne Johnson",

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AU - Bryant, R. M.

AU - Johnson, Marianne

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N2 - The Adams operations ψΛn and ψsn on the Green ring of a group G over a field K arise from the study of the exterior powers and symmetric powers of KG-modules. When G is finite and K has prime characteristic p we show that ψΛn and ψsn are periodic in n if and only if the Sylow p-subgroups of G are cyclic. In the case where G is a cyclic p-group we find the minimum periods and use recent work of Symonds to express ψSn in terms of ψΛn. © 2010 Elsevier B.V.

AB - The Adams operations ψΛn and ψsn on the Green ring of a group G over a field K arise from the study of the exterior powers and symmetric powers of KG-modules. When G is finite and K has prime characteristic p we show that ψΛn and ψsn are periodic in n if and only if the Sylow p-subgroups of G are cyclic. In the case where G is a cyclic p-group we find the minimum periods and use recent work of Symonds to express ψSn in terms of ψΛn. © 2010 Elsevier B.V.

U2 - 10.1016/j.jpaa.2010.07.005

DO - 10.1016/j.jpaa.2010.07.005

M3 - Article

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VL - 215

SP - 989

EP - 1002

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

IS - 5

ER -

Periodicity of Adams operations on the Green ring of a finite group

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