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.
A Note on the Nilpotency Class of the Unit Group of a Modular Group Algebra
CATINO, Francesco;SICILIANO, Salvatore;SPINELLI, Ernesto
2008-01-01
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.File in questo prodotto:
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