Let F be a field of characteristic p not equal 2 and G a group without 2- elements having an involution *. Write (FG)^(+) for the set of elements in the group ring FG that are symmetric with respect to the induced involution. In the present note, 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 not equal 3 and (FG)^(+) is Lie metabelian, then G must be abelian. This extends a result of Levin and Rosenberger.
Group algebras whose symmetric elements are Lie metabelian / Francesco, Catino; Gregory T., Lee; Spinelli, Ernesto. - In: FORUM MATHEMATICUM. - ISSN 0933-7741. - STAMPA. - 26:5(2014), pp. 1459-1471. [10.1515/forum-2012-0005]
Group algebras whose symmetric elements are Lie metabelian
SPINELLI, ERNESTO
2014
Abstract
Let F be a field of characteristic p not equal 2 and G a group without 2- elements having an involution *. Write (FG)^(+) for the set of elements in the group ring FG that are symmetric with respect to the induced involution. In the present note, 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 not equal 3 and (FG)^(+) is Lie metabelian, then G must be abelian. This extends a result of Levin and Rosenberger.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
