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Let M be a finitely generated metabelian group explicitly presented in a variety A2 of all
metabelian groups. An algorithm is constructed which, for every endomorphism ϕ ∈ End(M)
identical modulo an Abelian normal subgroup N containing the derived subgroup M and for any
pair of elements u, v ∈ M, decides if an equation of the form (xϕ)u = vx has a solution in M.
Thus, it is shown that the title problem under the assumptions made is algorithmically decidable.
Moreover, the twisted conjugacy problem in any polycyclic metabelian group M is decidable for
an arbitrary endomorphism ϕ ∈ End(M)
CitationVentura, E.; Romankov, V. Twisted conjugacy problem for endomorphisms of metabelian groups. "Algebra and Logic", 01 Març 2009, vol. 48, núm. 2, p. 89-98.
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