Algebra and Logic

, Volume 48, Issue 2, pp 89–98

The twisted conjugacy problem for endomorphisms of metabelian groups

Authors

    • University Politécnica de Catalunya
  • V. A. Roman’kov
    • Dostoevskii Omsk State University
Article

DOI: 10.1007/s10469-009-9048-y

Cite this article as:
Ventura, E. & Roman’kov, V.A. Algebra Logic (2009) 48: 89. doi:10.1007/s10469-009-9048-y

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).

Keywords

metabelian grouptwisted conjugacyendomorphismfixed pointsFox derivatives

Copyright information

© Springer Science+Business Media, Inc. 2009