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

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).
Giambruno, A., Polcino Milies, C., Sehgal, S. (2009). Lie properties of symmetric elements in group rings. JOURNAL OF ALGEBRA, 321(3), 890-902.
File in questo prodotto:
File Dimensione Formato  
Giambruno,Polcino,Sehgal-2009-JA 2.pdf

Solo gestori archvio

Dimensione 216.72 kB
Formato Adobe PDF
216.72 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
Giambruno,Polcino,Sehgal-2009-JA 2.pdf

accesso aperto

Dimensione 216.72 kB
Formato Adobe PDF
216.72 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10447/40086
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 26
  • ???jsp.display-item.citation.isi??? ND
social impact