The twisted conjugacy problem for pairs of endomorphisms in nilpotent groups

Details The twisted conjugacy problem for pairs of endomorphisms in nilpotent groups The twisted conjugacy problem for pairs of endomorphisms in nilpotent groups

2009-10-19

arxiv.org/abs/0910.3463v1

Mathematics

Group Theory

Scientific paper

An algorithm is constructed that, when given an explicit presentation of a finitely generated nilpotent group $G,$ decides for any pair of endomorphisms $\varphi, \psi : G \to G$ and any pair of elements $u, v \in G,$ whether or not the equation $(x\varphi)u = v (x\psi)$ has a solution $x \in G.$ Thus it is shown that the problem of the title is decidable. Also we present an algorithm that produces a finite set of generators of the subgroup (equalizer) $Eq_{\varphi, \psi}(G) \leq G$ of all elements $u \in G$ such that $u \varphi = u \psi .$

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