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Bulletin of the London Mathematical Society 2004 36(1):30-36; doi:10.1112/S0024609303002601
© 2004 by London Mathematical Society
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© London Mathematical Society

On the Commutator Width of Perfect Groups

Nikolay Nikolov

Tata Institute for Fundamental Research Colaba, Mumbai 400 005, India; nikinbg{at}abv.bg

Received 24 April 2002. Revision received 22 January 2003.

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.


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