Generalized Lie nilpotent group rings
Sbornik. Mathematics, Tome 57 (1987) no. 1, pp. 165-169
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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.
@article{SM_1987_57_1_a9,
author = {A. A. Bovdi and I. I. Khripta},
title = {Generalized {Lie} nilpotent group rings},
journal = {Sbornik. Mathematics},
pages = {165--169},
year = {1987},
volume = {57},
number = {1},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_1987_57_1_a9/}
}
A. A. Bovdi; I. I. Khripta. Generalized Lie nilpotent group rings. Sbornik. Mathematics, Tome 57 (1987) no. 1, pp. 165-169. http://geodesic.mathdoc.fr/item/SM_1987_57_1_a9/