GROUP ALGEBRAS WHOSE UNIT GROUP IS LOCALLY NILPOTENT
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.
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| Veröffentlicht in: | Journal of the Australian Mathematical Society (2001) 2020-08, Vol.109 (1), p.17-23 |
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| Format: | Artikel |
| Sprache: | eng |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | 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. |
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| ISSN: | 1446-7887 1446-8107 |
| DOI: | 10.1017/S1446788719000557 |