Finitely generated infinite simple groups of infinite square width and vanishing stable commutator length

Abstract

It is shown that there exist finitely generated infinite simple groups of infinite commutator width and infinite square width on which there exists no stably unbounded conjugation-invariant norm, and in particular stable commutator length vanishes. Moreover, a recursive presentation of such a group with decidable word and conjugacy problems is constructed.

v4: 41 pages, 6 figures rescaled at 120%; references updated, typos corrected, other minor corrections. v3: minor changes to the title, text and figures. v2: 41 pages, 6 figures; correction: Ore's conjecture was proved in 2008; 2 references added. v1: 40 pages, 6 figures

References in corpus (2)

• Finitely generated infinite simple groups of infinite commutator width
• Diagrams with Selection and Method for Constructing Boundedly Generated and Boundedly Simple Groups

Cited by in corpus (4)

• Word equations in simple groups and polynomial equations in simple algebras
• Cancelation norm and the geometry of biinvariant word metrics
• The winding invariant
• A remark on groups without finite quotients