On the Commutator Width of Perfect Groups

This paper proves bounds for the commutator width of a wreath product of two groups. As a corollary, it is shown that the commutator width of finite perfect linear groups of dimension 15 is unbounded. It follows that the covering number of these groups is unbounded. On the other hand, the commutator width of iterated wreath products of nonabelian finite simple groups is bounded by an absolute constant. 2000 Mathematics Subject Classification 20E22, 20E45.