A Survey on *-Group Identities on Units of Group Rings

Abstract

Let F be an infinite field of characteristic different from 2 and G a torsion group. Let the group ring FG have an involution induced from an involution on G. We survey recent results establishing the conditions under which the unit group of FG satisfies a *-group identity. The surprising outcome is that the unit group satisfies a *-group identity if and only if the symmetric units of FG satisfy a group identity.

Key Words:

• Group identity
• Group ring
• Involution
• Unit group

2010 Mathematics Subject Classification:

• 16U60
• 20C07
• 16W10

Notes

Communicated by S. Sehgal.