On the exponent of the Schur multiplier

The Schur multiplier is a very interesting invariant, being the archetype of group cohomology.
An explicit description of the multiplier is often too difficult a task.  Therefore it is of interest to obtain information about its arithmetical features, such as the order, the rank, and the exponent.
I will present the problem of bounding the exponent of the multiplier of a finite group, introducing the new concept of unitary cover.