The unitary cover of a finite group and the exponent of the Schur multiplier

For a finite group we introduce a particular central extension, the unitary cover, having minimal exponent among those satisfying the projective lifting property. We obtain new bounds for the exponent of the Schur multiplier relating to subnormal series, and we discover new families for which the bound is the exponent of the group. Finally, we show that unitary covers are controlled by the Zelmanov solution of the restricted Burnside problem for 2-generator groups.