Bounds for the exponent of the Schur multiplier

This article introduces new techniques and theorems pertaining to the powers of the unitary cocycles, the power structure of the unitary cover, and their relation to general central extensions. In turn, bounds for the exponent of the Schur multiplier and the unitary cover are provided in terms of the nilpotency class, the rank, and the coclass of the underlying group. Moreover, the quadratic bound (exp⁡G)2 holds whenever exp⁡G≤7. Finally, the problem of describing bounds is related to the study of symmetric invariant 2-cocycles.