Geodesic
On solvability of equations with endomorphisms in nilpotent groups
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 13 (2016), pp. 716-725

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We prove that the conjugacy, twisted conjugacy and bi-twisted conjugacy problems, and the corresponding search problems, are decidable for the class $\mathbf{N}_{fg} $ of all finitely generated nilpotent groups. Also we give a finite description of the equalizer of any pair of endomorphisms of arbitrary group in the class $\mathbf{N}_{fg}$.
Keywords: finitely generated group, (twisted, bi-twisted) conjugacy problem, search problems, fix-point and equalizer problems, algorithm, complexity. 
@article{SEMR_2016_13_a19,
     author = {V. A. Roman'kov},
     title = {On solvability of equations with endomorphisms in nilpotent groups},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {716--725},
     publisher = {mathdoc},
     volume = {13},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2016_13_a19/}
}
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V. A. Roman'kov. On solvability of equations with endomorphisms in nilpotent groups. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 13 (2016), pp. 716-725. http://geodesic.mathdoc.fr/item/SEMR_2016_13_a19/