Let $F$ be a field of characteristic different from $2$, and $G$ a group with involution $\ast$. Write $(FG)^+$ for the set of elements in the group ring $FG$ that are symmetric with respect to the induced involution. Recently, Giambruno, Polcino Milies and Sehgal [\emph{Lie properties of symmetric elements in group rings}, J. Algebra {\bf 321} (2009), 890-902] showed that if $G$ has no $2$-elements, and $(FG)^+$ is Lie nilpotent (resp. Lie $n$-Engel), then $FG$ is Lie nilpotent (resp. Lie $m$-Engel, for some $m$). Here, we classify the groups containing $2$-elements such that $(FG)^+$ is Lie nilpotent or Lie $n$-Engel.
Lie properties of symmetricelements in group rings II
SPINELLI, Ernesto
2009-01-01
Abstract
Let $F$ be a field of characteristic different from $2$, and $G$ a group with involution $\ast$. Write $(FG)^+$ for the set of elements in the group ring $FG$ that are symmetric with respect to the induced involution. Recently, Giambruno, Polcino Milies and Sehgal [\emph{Lie properties of symmetric elements in group rings}, J. Algebra {\bf 321} (2009), 890-902] showed that if $G$ has no $2$-elements, and $(FG)^+$ is Lie nilpotent (resp. Lie $n$-Engel), then $FG$ is Lie nilpotent (resp. Lie $m$-Engel, for some $m$). Here, we classify the groups containing $2$-elements such that $(FG)^+$ is Lie nilpotent or Lie $n$-Engel.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.
