Geodesic
Embeddings of partially commutative nilpotent groups
Matematičeskie zametki, Tome 116 (2024) no. 2, pp. 236-244.

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We present an algorithm determining the existence of an isomorphic embedding of one finitely generated partially commutative nilpotent group of class $2$ in another. It is shown how such embeddings can be constructed. We also describe an algorithm determining the existence of an embedding of a finitely generated partially commutative nilpotent group of arbitrary class $l$ with respect to a graph of nonzero radius in a free nilpotent group of class $l$.
Keywords: nilpotent group, partially commutative group, embedding. 
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A. L. Evtyagin; V. A. Roman'kov. Embeddings of partially commutative nilpotent groups. Matematičeskie zametki, Tome 116 (2024) no. 2, pp. 236-244. http://geodesic.mathdoc.fr/item/MZM_2024_116_2_a5/

[1] V. A. Romankov, “Vlozhenie svobodnykh nilpotentnykh (metabelevykh) grupp v chastichno kommutativnye nilpotentnye (metabelevy) gruppy”, Matem. zametki, 114:5 (2023), 773–779 | DOI

[2] R. Charney, “An introduction to right-angled Artin groups”, Geom. Dedicata, 125 (2007), 141–158 | DOI | MR

[3] A. J. Duncan, V. N. Remeslennikov, A. V. Treier, “A survey of free partially commutative groups”, J. Physics. Conference Ser., 1441 (2020), 012136 | DOI

[4] C. Droms, “Isomorphisms of graph groups”, Proc. Amer. Math. Soc., 100 (1987), 407–408 | DOI | MR

[5] E. I. Timoshenko, “Mal'tsev bases for partially commutative nilpotent groups”, Internat. J. Algebra Comput., 32:1 (2021), 1–9 | DOI | MR

[6] A. I. Maltsev, “Dva zamechaniya o nilpotentnykh gruppakh”, Matem. sb., 37 (79):3 (1955), 567–572 | MR | Zbl

[7] M. I. Kargapolov, Yu. I. Merzlyakov, Osnovy teorii grupp, Nauka, M., 1972 | MR

[8] Ph. Hall, The Edmonton Notes on Nilpotent Groups, Queen Mary College Mathematics Notes, Queen Mary College, London, 1969 | MR

[9] B. Magnus, A. Karrass, D. Solitar, Combinatorial Group Theory: Presentations of Groups in Terms of Generators and Relations, Interscience Publ., New York, 1966 | MR