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GROUP ALGEBRAS WHOSE GROUP OF UNITS IS POWERFUL

Part of: Representation theory of groups Conditions on elements

Published online by Cambridge University Press:  15 December 2009

VICTOR BOVDI
VICTOR BOVDI*
Affiliation:
Institute of Mathematics, University of Debrecen, H-4010 Debrecen, P.O.B. 12, Institute of Mathematics and Informatics, College of Nyíregyháza, Sóstói út 31/b, H-4410 Nyíregyháza, Hungary (email: vbovdi@math.klte.hu)
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Abstract

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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

modular group algebragroup of unitspowerful grouppro-p-group

MSC classification

Secondary: 20C05: Group rings of finite groups and their modules 16U60: Units, groups of units
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 87 , Issue 3 , December 2009 , pp. 325 - 328
Copyright
Copyright © Australian Mathematical Publishing Association, Inc. 2009

References

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