Algebra and Logic

, Volume 48, Issue 2, pp 89-98

First online:

The twisted conjugacy problem for endomorphisms of metabelian groups

  • E. VenturaAffiliated withUniversity Politécnica de Catalunya Email author 
  • , V. A. Roman’kovAffiliated withDostoevskii Omsk State University

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access

Let M be a finitely generated metabelian group explicitly presented in a variety \( {\mathcal{A}}^2 \) 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, vM, decides if an equation of the form ()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).


metabelian group twisted conjugacy endomorphism fixed points Fox derivatives