Geodesic
Embedding of Free Nilpotent~(Metabelian) Groups in Partially Commutative Nilpotent (Metabelian) Groups
Matematičeskie zametki, Tome 114 (2023) no. 5, pp. 773-779.

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An algorithm is presented that determines the maximum rank of a free nilpotent metabelian or, respectively, nilpotent group isomorphically embeddable into a given partially commutative nilpotent group of the same degree of nilpotency. It is shown how these embeddings are realized.
Keywords: nilpotent group, metabelian group, partially commutative group, free group, embedding. 
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     author = {V. A. Roman'kov},
     title = {Embedding of {Free} {Nilpotent~(Metabelian)} {Groups} in {Partially} {Commutative} {Nilpotent} {(Metabelian)} {Groups}},
     journal = {Matemati\v{c}eskie zametki},
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V. A. Roman'kov. Embedding of Free Nilpotent~(Metabelian) Groups in Partially Commutative Nilpotent (Metabelian) Groups. Matematičeskie zametki, Tome 114 (2023) no. 5, pp. 773-779. http://geodesic.mathdoc.fr/item/MZM_2023_114_5_a9/

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

[2] A. J Duncan, V. N. Remeslennikov, A. V. Treier, “A survey of Free Partially Commutative Groups”, J. Phys.: Conf. Ser., 1441 (2020), 012136 | DOI

[3] C. Droms, “Isomorphisms of graph groups”, Proc. Amer. Math. Soc., 100:3 (1987), 407–408 | DOI | MR

[4] E. I. Timoshenko, “Maltsevskaya baza chastichno kommutativnoi nilpotentnoi metabelevoi gruppy”, Algebra i logika, 50:5 (2011), 647–658 | MR | Zbl

[5] E. I. Timoshenko, “Mal'tsev bases for partially commutative nilpotent groups”, Internat. J. Algebra Comput., 32:1 (2022), 1–9 | DOI | MR

[6] V. A. Romankov, “Ob uravneniyakh v svobodnykh metabelevykh gruppakh”, Sib. matem. zhurn., 20:3 (1979), 671–673 | MR | Zbl

[7] V. A. Romankov, “O nerazreshimosti problemy endomorfnoi svodimosti v svobodnykh nilpotentnykh gruppakh i svobodnykh koltsakh”, Algebra i logika, 16:4 (1977), 457–471 | MR

[8] V. A. Romankov, “Nerazreshimost problemy vkhozhdeniya v podmonoid svobodnoi nilpotentnoi gruppy stupeni $l\geq 2$ dostatochno bolshogo ranga”, Izv. RAN. Ser. matem., 87:4 (2023), 166–185 | DOI

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

[10] G. Baumslag, “Some subgroup theorems for free $\mathfrak{b}$-groups”, Trans. Amer. Math. Soc., 108 (1963), 516–525 | MR

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

[12] Ph. Hall, The Edmonton Notes on Nilpotent Groups (University of Alberta, 1957), Queen Mary College, London, 1969 | MR