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This article is cited in 8 scientific papers (total in 8 papers)
Nilpotency of the multiplicative group of a group ring
I. I. Khripta Uzhgorod State University
Abstract:
It is proven that if $K$ is a commutative ring of characteristic $p^m$ while group $G$ contains $p$-elements, then the multiplicative group $UKG$ of group ring $KG$ is nilpotent if and only if $G$ is nilpotent and its commutant $G'$ is a finite $p$-group. Those group algebras $KG$ are described for which the nilpotency classes of groups $G$ and $UKG$ coincide.
Received: 28.09.1970
Citation:
I. I. Khripta, “Nilpotency of the multiplicative group of a group ring”, Mat. Zametki, 11:2 (1972), 191–200; Math. Notes, 11:2 (1972), 119–124
Linking options:
https://www.mathnet.ru/eng/mzm9779 https://www.mathnet.ru/eng/mzm/v11/i2/p191
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Abstract page: | 192 | Full-text PDF : | 81 | First page: | 1 |
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