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This article is cited in 12 scientific papers (total in 12 papers)
Generalized Lie nilpotent group rings
A. A. Bovdi, I. I. Khripta
Abstract:
Let $KG$ be the group ring of a group $G$ over a ring $K$ with identity. The ring $KG$ is said to be Lie $T$-nilpotent if for every sequence $x_1,x_2,\dots,x_n,\dots$ of elements of $KG$ there is an index $m$ such that the Lie commutator $(\dots((x_1,x_2),x_3)\dots,x_m)=0$. It is proved that $KG$ is a Lie $T$-nilpotent ring if and only if $K$ is Lie $T$-nilpotent and one of the following conditions is satisfied: 1) $G$ is an Abelian group, or 2) $K$ is a ring of characteristic $p^m$ ($p$ prime), $G$ is a nilpotent group and its commutator subgroup is a finite $p$-group.
Bibliography: 3 titles.
Received: 23.10.1984
Citation:
A. A. Bovdi, I. I. Khripta, “Generalized Lie nilpotent group rings”, Mat. Sb. (N.S.), 129(171):1 (1986), 154–158; Math. USSR-Sb., 57:1 (1987), 165–169
Linking options:
https://www.mathnet.ru/eng/sm1812https://doi.org/10.1070/SM1987v057n01ABEH003061 https://www.mathnet.ru/eng/sm/v171/i1/p154
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Abstract page: | 303 | Russian version PDF: | 96 | English version PDF: | 7 | References: | 32 |
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