Infinite simple groups of large commutator width
by
Alexey Muranov
Vanderbilt University Deptartment of Mathematics 1326 Stevenson Center

In 1977, I. M. Isaacs asked if there exists a non-abelian simple group containing an element which is not a commutator. In terms of commutator width, the question is whether there exist simple groups of commutator width greater than 1.

We show how to construct simple groups of arbitrarily large commutator width, presenting such groups by generators and defining relations.

Date received: March 13, 2006