6533b7d5fe1ef96bd1263c84

RESEARCH PRODUCT

Star-group identities and groups of units

subject

description

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 ≠ 2. Extend * linearly to FG. We prove that the unit group \({\mathcal{U}}\) of FG satisfies a *-identity if and only if the symmetric elements \({\mathcal{U}^+}\) satisfy a group identity.