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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On the number of generators and the modular group-ring of a finite $ p$-group


Authors: Olaf Manz and Reiner Staszewski
Journal: Proc. Amer. Math. Soc. 98 (1986), 189-195
MSC: Primary 20C05; Secondary 16A26, 20C20
DOI: https://doi.org/10.1090/S0002-9939-1986-0854016-4
MathSciNet review: 854016
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Abstract: We consider the Loewy-series $ J{(KP)^i}$ of a finite $ p$-group $ P$ over a field $ K$ of characteristic $ p$. We point that the series is not 'monotonic' in general, but we can show that the dimensions of the Loewy-factors $ J{(KP)^i}/J{(KP)^{i + 1}}$ (except the first and the last one) are greater than or equal to the minimal number of generators of $ P$.


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DOI: https://doi.org/10.1090/S0002-9939-1986-0854016-4
Keywords: This paper is a contribution to the research project "Darstellungstheorie" of the DFG
Article copyright: © Copyright 1986 American Mathematical Society