Finitely generated infinite simple groups of infinite commutator width

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

References in corpus (2)

• Diagrams with Selection and Method for Constructing Boundedly Generated and Boundedly Simple Groups
• On torsion-free groups with finite regular file bases

Cited by in corpus (5)

• Word equations in simple groups and polynomial equations in simple algebras
• Finitely generated infinite simple groups of infinite square width and vanishing stable commutator length
• Irreducible Bases and Subgroups of a Wreath Product in Applying to Diffeomorphism Groups acting on the Möbius Band
• Independence property and hyperbolic groups
• Homomorphisms on infinite direct products of groups, rings and monoids