Star-group identities and groups of units

Analogous to *-identities in rings with involution we define *-identities in groups. Suppose that G is a torsion group with involution * and that F is an infinite field with char F not equal 2. Extend * linearly to FG. We prove that the unit group U of FG satisfies a *-identity if and only if the symmetric elements U(+) satisfy a group identity.

MIUR of Italy

MIUR of Italy

FAPESP[Proc. 2009/52665-0]

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

CNPq[Proc. 300243/79-0]

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

NSERC

NSERC