Let $^*$ be an involution of a group $G$ extended linearly to the group algebra $KG$. We prove that if $G$ contains no $2$-elements and $K$ is a field of characteristic $p\neq 2$, then the $*$-symmetric elements of $KG$ are Lie nilpotent (Lie $n$-Engel) if and only if $KG$ is Lie nilpotent (Lie $n$-Engel).
Giambruno, A., Polcino Milies, C., Sehgal, S. (2009). Lie properties of symmetric elements in group rings. JOURNAL OF ALGEBRA, 321(3), 890-902.
Lie properties of symmetric elements in group rings
GIAMBRUNO, Antonino;
2009-01-01
Abstract
Let $^*$ be an involution of a group $G$ extended linearly to the group algebra $KG$. We prove that if $G$ contains no $2$-elements and $K$ is a field of characteristic $p\neq 2$, then the $*$-symmetric elements of $KG$ are Lie nilpotent (Lie $n$-Engel) if and only if $KG$ is Lie nilpotent (Lie $n$-Engel).
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