It is well known that a modular group algebra $KG$ is Lie nilpotent if, and only if, its unit group $\mathcal{U}(KG)$ is nilpotent. In this note we prove that, if $G$ is a torsion group, then the equality $cl_L(KG)=\mbox{cl}(\mathcal{U}(KG))$ occurs.
Titolo: | A Note on the Nilpotency Class of the Unit Group of a Modular Group Algebra |
Autori: | |
Data di pubblicazione: | 2008 |
Rivista: | |
Abstract: | It is well known that a modular group algebra $KG$ is Lie nilpotent if, and only if, its unit group $\mathcal{U}(KG)$ is nilpotent. In this note we prove that, if $G$ is a torsion group, then the equality $cl_L(KG)=\mbox{cl}(\mathcal{U}(KG))$ occurs. |
Handle: | http://hdl.handle.net/11587/107528 |
Appare nelle tipologie: | Articolo pubblicato su Rivista |
File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.