Groups, Geometry, and Dynamics


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Volume 4, Issue 3, 2010, pp. 407–417
DOI: 10.4171/GGD/88

Published online: 2010-06-16

A recursive presentation for Mihailova’s subgroup

Oleg Bogopolski[1] and Enric Ventura[2]

(1) Heinrich-Heine-Universität, Düsseldorf, Germany
(2) Universitat Politècnica de Catalunya, Manresa (Barcelona), Spain

An explicit recursive presentation for Mihailova’s subgroup M(H) of Fn × Fn corresponding to a finite, concise and Peiffer aspherical presentation H = < x1, … , xn | R1, … , Rm > is given. This partially answers a question of R. I. Grigorchuk. As a corollary, we construct a finitely generated recursively presented orbit undecidable subgroup of Aut(F3).

Keywords: Mihailova’s subgroup, recursive presentation, asphericity, orbit undecidability

Bogopolski Oleg, Ventura Enric: A recursive presentation for Mihailova’s subgroup. Groups Geom. Dyn. 4 (2010), 407-417. doi: 10.4171/GGD/88