Group algebras whose group of units is powerful

Victor Bovdi

doi:10.1017/S1446788709000214

Group algebras whose group of units is powerful

Victor Bovdi

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

1 Citation (Scopus)

Abstract

A p-group is called powerful if every commutator is a product of pth powers when p is odd and a product of fourth powers when p=2. In the group algebra of a group G of p-power order over a finite field of characteristic p, the group of normalized units is always a p-group. We prove that it is never powerful except, of course, when G is abelian.

Original language	English
Pages (from-to)	325-328
Number of pages	4
Journal	Journal of the Australian Mathematical Society
Volume	87
Issue number	3
DOIs	https://doi.org/10.1017/S1446788709000214
Publication status	Published - Dec 2009
Externally published	Yes

Keywords

Group of units
Modular group algebra
Powerful group
Pro-p-group

ASJC Scopus subject areas

General Mathematics

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10.1017/S1446788709000214

Cite this

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title = "Group algebras whose group of units is powerful",

abstract = "A p-group is called powerful if every commutator is a product of pth powers when p is odd and a product of fourth powers when p=2. In the group algebra of a group G of p-power order over a finite field of characteristic p, the group of normalized units is always a p-group. We prove that it is never powerful except, of course, when G is abelian.",

keywords = "Group of units, Modular group algebra, Powerful group, Pro-p-group",

author = "Victor Bovdi",

note = "Funding Information: The research was supported by OTKA No. K68383. {\textcopyright}c 2009 Australian Mathematical Publishing Association, Inc. 1446-7887/2009 \$16.00",

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N2 - A p-group is called powerful if every commutator is a product of pth powers when p is odd and a product of fourth powers when p=2. In the group algebra of a group G of p-power order over a finite field of characteristic p, the group of normalized units is always a p-group. We prove that it is never powerful except, of course, when G is abelian.

AB - A p-group is called powerful if every commutator is a product of pth powers when p is odd and a product of fourth powers when p=2. In the group algebra of a group G of p-power order over a finite field of characteristic p, the group of normalized units is always a p-group. We prove that it is never powerful except, of course, when G is abelian.

KW - Group of units

KW - Modular group algebra

KW - Powerful group

KW - Pro-p-group

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DO - 10.1017/S1446788709000214

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JF - Journal of the Australian Mathematical Society

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ER -

Group algebras whose group of units is powerful

Abstract

Keywords

ASJC Scopus subject areas

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