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Q-PERFECT GROUPS AND UNIVERSAL Q-CENTRAL EXTENSIONS Using results of Ellis-Rodríguez Fernández, an explicit description by generators and relations is given of the mod q Schur multiplier, and this is shown to be the kernel of a universal q-central extension in the case of a q-perfect group, i .e . one which is generated by commutators and q-th powers . These results generalise earlier work K . Dennis and Brown-Loday.doi:10.5565/publmat_34290_08 fatcat:6otkc7cbzjhwta72i4ptjbnkpq