Let F be a field of characteristic p ≠ 2 and G a group without 2-elements having an involution *. Extend the involution linearly to the group ring FG, and let (FG)^- denote the set of skew elements with respect to *-. In this paper, we show that if G is finite and (FG)^- is Lie metabelian, then G is nilpotent. Based on this result, we deduce that if G is torsion, p > 7 and (FG)^- is Lie metabelian, then G must be abelian. Exceptions are constructed for smaller values of p.
Lie metabelian skew elements in group rings / Gregory T., Lee; Spinelli, Ernesto. - In: GLASGOW MATHEMATICAL JOURNAL. - ISSN 0017-0895. - STAMPA. - 56:1(2014), pp. 187-195. [10.1017/s0017089513000165]
Lie metabelian skew elements in group rings
SPINELLI, ERNESTO
2014
Abstract
Let F be a field of characteristic p ≠ 2 and G a group without 2-elements having an involution *. Extend the involution linearly to the group ring FG, and let (FG)^- denote the set of skew elements with respect to *-. In this paper, we show that if G is finite and (FG)^- is Lie metabelian, then G is nilpotent. Based on this result, we deduce that if G is torsion, p > 7 and (FG)^- is Lie metabelian, then G must be abelian. Exceptions are constructed for smaller values of p.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
