Identidades de grupo em unidades de Anel de Grupo

Abstract

In this work, we address the confirmation of Brian Hartley's conjecture, namely: "Let K be a body and G a torsion group. If U (KG), the group of units of group algebra KG, satisfies a group identity, then KG satisfies a polynomial identity. We study the particular case of this conjecture, closely following the work entitled "Group identities on units of rings", by Antônio Giambruno, Eric Jespers and Ângela Valenti, who proved the Hartley conjecture for group rings RG over an infinite commutative domain R of characteristic $p\ge0$ and G a p'-torsion group.