Geodesic
Centralizer dimensions and universal theories for partially commutative metabelian groups
Algebra i logika, Tome 56 (2017) no. 2, pp. 226-255.

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Centralizer dimensions are computed for partially commutative metabelian groups $S_\Gamma$ whose defining graphs $\Gamma$ are trees. Universal theories of partially commutative metabelian groups defined by cycles and linear graphs are studied.
Keywords: partially commutative metabelian group, centralizer dimension, defining graph, universal theory. 
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E. I. Timoshenko. Centralizer dimensions and universal theories for partially commutative metabelian groups. Algebra i logika, Tome 56 (2017) no. 2, pp. 226-255. http://geodesic.mathdoc.fr/item/AL_2017_56_2_a5/

[1] Ch. K. Gupta, E. I. Timoshenko, “Chastichno kommutativnye metabelevy gruppy: tsentralizatory i elementarnaya ekvivalentnost”, Algebra i logika, 48:3 (2009), 309–341 | MR | Zbl

[2] E. I. Timoshenko, “Universalnaya ekvivalentnost chastichno kommutativnykh metabelevykh grupp”, Algebra i logika, 49:2 (2010), 263–290 | MR | Zbl

[3] Ch. K. Gupta, E. I. Timoshenko, “Ob universalnykh teoriyakh chastichno kommutativnykh metabelevykh grupp”, Algebra i logika, 50:1 (2011), 3–25 | MR | Zbl

[4] E. I. Timoshenko, Endomorfizmy i universalnye teorii razreshimykh grupp, Izd-vo NGTU, Novosibirsk, 2011

[5] R. M. Bryant, “Groups with the minimal condition on centralizers”, J. Algebra, 60:2 (1979), 371–383 | DOI | MR | Zbl

[6] A. Myasnikov, P. Shumyatsky, “Discriminating groups and $c$-dimension”, J. Group Theory, 7:1 (2004), 135–142 | MR | Zbl

[7] R. Schmidt, “Zentralisatorverbände endlicher Gruppen”, Rend. Sem. Mat. Univ. Padova, 44 (1971), 97–131 | MR | Zbl

[8] A. J. Duncan, I. V. Kazachkov, V. N. Remeslennikov, “Centraliser dimension and universal classes of groups”, Sib. elektron. matem. izv., 3 (2006), 197–215 | MR | Zbl

[9] A. J. Duncan, I. V. Kazachkov, V. N. Remeslennikov, “Centraliser dimension of partially commutative groups”, Geom. Dedicata, 120 (2006), 73–97 | DOI | MR | Zbl

[10] A. H. Rhemtulla, “Commutators of certain finitely generated soluble groups”, Can. J. math., 21:5 (1969), 1160–1164 | DOI | MR | Zbl

[11] A. A. Mischenko, E. I. Timoshenko, “Universalnaya ekvivalentnost chastichno kommutativnykh nilpotentnykh grupp”, Sib. matem. zh., 52:5 (2011), 1113–1122 | MR

[12] E. I. Timoshenko, “K voprosu ob elementarnoi ekvivalentnosti grupp”, Algebra, v. 1, Irkutskii gos. un-t, 1972, 92–96

[13] E. I. Timoshenko, “Ob universalno ekvivalentnykh razreshimykh gruppakh”, Algebra i logika, 39:2 (2000), 227–240 | MR | Zbl

[14] E. R. Green, Graph products of groups, PhD Thesis, Univ. Leeds, 1990

[15] L. J. Corredor, M. A. Gutierrez, “A generating set for the automorphism group of a graph product of Abelian groups”, Int. J. Algebra Comput., 22:1 (2012), 1250003, 21 pp. | DOI | MR | Zbl

[16] R. Charney, K. Ruane, N. Stambaugh, A. Vijayan, “The automorphism group of a graph product with no SIL”, Ill. J. Math., 54:1 (2010), 249–262 | MR | Zbl