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On the Commutator Width of Perfect Groups
Author(s) -
Nikolov Nikolay
Publication year - 2004
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609303002601
Subject(s) - mathematics , commutator , wreath product , iterated function , commutator subgroup , pure mathematics , corollary , simple (philosophy) , dimension (graph theory) , bounded function , constant (computer programming) , group (periodic table) , combinatorics , product (mathematics) , mathematical analysis , algebra over a field , geometry , normal subgroup , programming language , philosophy , chemistry , lie conformal algebra , organic chemistry , epistemology , computer science
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.