*-Group identities on units of division rings. Issue 7 (18th June 2021) - Bien, M. H.; Ramezan-Nassab, M.; Viet, D. H.
Abstract: Let D be a division ring with infinite center F . By a well known result of Amitsur, if U ( D ) satisfies a group identity, then D is commutative. Now assume that D has an involution * of the first kind. In this paper, among other results, we show that if U ( D ) satisfies a *-group identity, then either D is commutative or dim F D = 4 and * is of the symplectic type. As a result, let N be a *-invariant normal subgroup of U ( D ) such that all symmetric elements of N are central (this is the case when, for example, each symmetric element of N is bounded Engel). Then either N is central or dim F D = 4 and * is of the symplectic type.