Meta-abelian unit groups of group algebras are usually abelian

Aner Shalev

doi:10.1016/0022-4049(91)90067-C

Meta-abelian unit groups of group algebras are usually abelian

Aner Shalev^*

^*Corresponding author for this work

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

17 Scopus citations

Abstract

Given a field F of positive characteristic p>2 and a finite group G we give necessary and sufficient conditions for the unit group of the group algebra FG to be meta-abelian. In particular, if p≥5, this happens only when G is abelian.

Original language	English
Pages (from-to)	295-302
Number of pages	8
Journal	Journal of Pure and Applied Algebra
Volume	72
Issue number	3
DOIs	https://doi.org/10.1016/0022-4049(91)90067-C
State	Published - 26 Jul 1991
Externally published	Yes

Bibliographical note

Funding Information:
I am grateful to Avinoam Mann for his helpful comments.I would also like to thank the Rothschild Foundation for financial support, and the Mathematical Institute at Oxford for its hospitality.

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10.1016/0022-4049(91)90067-C

Cite this

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title = "Meta-abelian unit groups of group algebras are usually abelian",

abstract = "Given a field F of positive characteristic p>2 and a finite group G we give necessary and sufficient conditions for the unit group of the group algebra FG to be meta-abelian. In particular, if p≥5, this happens only when G is abelian.",

author = "Aner Shalev",

note = "Funding Information: I am grateful to Avinoam Mann for his helpful comments.I would also like to thank the Rothschild Foundation for financial support, and the Mathematical Institute at Oxford for its hospitality.",

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AB - Given a field F of positive characteristic p>2 and a finite group G we give necessary and sufficient conditions for the unit group of the group algebra FG to be meta-abelian. In particular, if p≥5, this happens only when G is abelian.

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Meta-abelian unit groups of group algebras are usually abelian

Abstract

Bibliographical note

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