Finitely generated infinite simple groups of infinite commutator width
arXiv:math/0608688 · doi:10.1142/S0218196707003767
Abstract
It is shown that there exists a finitely generated infinite simple group of infinite commutator width, and that the commutator width of a finitely generated infinite boundedly simple group can be arbitrarily large. Besides, such groups can be constructed with decidable word and conjugacy problems.
v4: 49 pages, 2 figures, a couple of obvious mistakes corrected; v3: 49 pages, 2 figures; multiple corrections and improvements; added reference to John Wilson; numbering of theorems, equations, etc. is changed to match that of IJAC version; v2: 53 pages, 2 figures; corrections, improvements; minor changes in terminology and notation; v1: 54 pages