Mozgovoj, István (2026) A note on modular group algebras with metabelian unit groups in characteristic two Annales Mathematicae et Informaticae. ISSN 1787-6117 (Online)
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Absztrakt (kivonat)
Let F G denote the group algebra of a group G over a field F of characteristic 2, and let U(F G) denote its group of units. The classification of finite groups G for which U(F G) is metabelian is known, while the corresponding problem for infinite groups is considerably more delicate. We first complete the classification for torsion groups by removing the nilpotency assumption from an earlier result of Catino and Spinelli. We prove that, for a non-abelian torsion group G, the unit group U(F G) is metabelian if and only if either G ′ is a central elementary abelian group of order 2 or 4, or F is the field of two elements and G is an extension of an elementary abelian 3-group by a group of order 2 acting by inversion. Thus, in the torsion case, the classification coincides with that known for finite groups. We also investigate non-torsion groups and prove that if F G is modular and U(F G) is metabelian, then G must be nilpotent. This substantially restricts the possible new cases in the remaining non-torsion setting.
| Mű típusa: | Folyóiratcikk - Journal article |
|---|---|
| Szerző: | Szerző neve Email MTMT azonosító ORCID azonosító Közreműködés Mozgovoj, István NEM RÉSZLETEZETT NEM RÉSZLETEZETT NEM RÉSZLETEZETT Szerző |
| Megjegyzés: | This work was supported by the Collegium Talentum Programme of Hungary. - Accepted manuscript. Published online: October 23, 2026 |
| Kapcsolódó URL-ek: | |
| Kulcsszavak: | group rings, unit group, derived length |
| Nyelv: | angol |
| DOI azonosító: | 10.33039/ami.2026.10.002 |
| ISSN: | 1787-6117 (Online) |
| Felhasználó: | Tibor Gál |
| Dátum: | 24 Okt 2026 15:43 |
| Utolsó módosítás: | 24 Okt 2026 15:43 |
| URI: | http://publikacio.uni-eszterhazy.hu/id/eprint/9516 |
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