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).
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Oleg Bogopolski, Enric Ventura, A recursive presentation for Mihailova’s subgroup. Groups Geom. Dyn. 4 (2010), no. 3, pp. 407–417DOI 10.4171/GGD/88