Unitary units in modular group algebras
| dc.creator | Bovdi, V. A. | |
| dc.creator | Kovács, L. G. | |
| dc.date | 2007-11-01 | |
| dc.date.accessioned | 2026-07-07T08:39:53Z | |
| dc.date.available | 2026-07-07T08:39:53Z | |
| dc.description | Let p be a prime, K a field of characteristic p, G a locally finite p-group, KG the group algebra, and V the group of the units of KG with augmentation 1. The anti-automorphism g\mapsto g^{-1} of G extends linearly to KG; this extension leaves V setwise invariant, and its restriction to V followed by v\mapsto v^{-1} lives an automorphism of V. The elements of V fixed by this automorphism are called unitary; they form a subgroup. Our first theorem describes the K and G for which this subgroup is normal in V. For each element g in G, let \bar{g} denote the sum (in KG) of the distinct powers of g. The elements 1+(g-1)h\bar{g} with g,h\in G are the bicyclic units of KG. Our second theorem describes the K and G for which all bicyclic units are unitary. | |
| dc.description | 12 pages | |
| dc.identifier | https://arxiv.org/abs/0711.0097 | |
| dc.identifier | http://arxiv.org/abs/0711.0097 | |
| dc.identifier | Manuscripta Math. 84 (1994), no. 1, 57--72 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/141225 | |
| dc.subject | Rings and Algebras | |
| dc.subject | Group Theory | |
| dc.subject | 16U60; 16S34; 20C07 | |
| dc.title | Unitary units in modular group algebras | |
| dc.type | text |