Identidades polinomiais via identidades de grupo : a conjectura de Brian Hartley

Abstract

In this work, we present the Conjecture of Brian Hartley and study its validity, i.e, we verify if group identities in the unity group U(FG) make FG satisfy a polynomial identity, where G is a torsion group and F any field. This study will be made first for infinite fields, and next for any field. From this result, will be deduced necessary and suficient conditions in a group G, for the unity group U(FG) satisfy group identities.