We present a complete list of groups $G$ and fields $F$ for which: (i) the group of normalized units $V(FG)$ of the group algebra $FG$ is locally nilpotent; (ii) the set of nontrivial nilpotent elements of $FG$ is finite and nonempty, and $V(FG)$ is an Engel group.

中文翻译：

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组代数，其单位组在本地是 NILPOTENT

我们提供完整的组列表$G$和领域$F$其中： (i) 归一化单位组$V(FG)$群代数的$FG$是局部幂零的；(ii) 非平凡幂零元素的集合$FG$是有限且非空的，并且$V(FG)$是恩格尔群。