The twisted conjugacy problem for endomorphisms of metabelian groups |
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Authors: | E Ventura V A Roman’kov |
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Institution: | (1) University Politécnica de Catalunya, Av. Bases de Manresa 61-73, 08242— Manresa, Barcelona, Spain;(2) Dostoevskii Omsk State University, pr. Mira 55-A, Omsk, 644077, Russia |
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Abstract: | Let M be a finitely generated metabelian group explicitly presented in a variety 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).
Supported by RFBR (project No. 07-01-00392). (V. A. Roman’kov)
Translated from Algebra i Logika, Vol. 48, No. 2, pp. 157–173, March–April, 2009. |
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Keywords: | metabelian group twisted conjugacy endomorphism fixed points Fox derivatives |
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