Geodesic
Centralizer dimensions of partially commutative metabelian groups
Algebra i logika, Tome 57 (2018) no. 1, pp. 102-117

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We establish an upper bound for the centralizer dimension of a partially commutative metabelian group that depends linearly on the number of vertices in a defining graph. It is proved that centralizer dimensions of $2$-generated metabelian groups are not bounded above. The exact value of the centralizer dimension is computed for a partially commutative metabelian group defined by a cycle.
Keywords: partially commutative metabelian group, centralizer dimension, defining graph. 
@article{AL_2018_57_1_a5,
     author = {E. I. Timoshenko},
     title = {Centralizer dimensions of partially commutative metabelian groups},
     journal = {Algebra i logika},
     pages = {102--117},
     publisher = {mathdoc},
     volume = {57},
     number = {1},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2018_57_1_a5/}
}
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E. I. Timoshenko. Centralizer dimensions of partially commutative metabelian groups. Algebra i logika, Tome 57 (2018) no. 1, pp. 102-117. http://geodesic.mathdoc.fr/item/AL_2018_57_1_a5/