Infinite simple characteristic quotients

Abstract

We construct continuum many infinite, simple, characteristic quotients of non-abelian free groups, answering a 1978 question of James Wiegold. The method is very flexible, allowing to impose certain properties on the quotients, to generalize the construction to large classes of groups with hyperbolic features, and to produce quasi-isometrically diverse examples.

arXiv comment24 pages. v2: added results on quasi-isometric diversity. v3: all groups constructed are now 2-generated. v4: accepted version, to appear in Journal de l'Ecole polytechnique