Geodesic
Universal theories and centralizer dimensions of groups
Algebra i logika, Tome 58 (2019) no. 3, pp. 397-416

Voir la notice de l'article provenant de la source Math-Net.Ru

The exact value of the centralizer dimension is found for a free polynilpotent group and for a free group in a variety of metabelian groups of nilpotency class at most $c$. Relations between $\exists$- and $\Phi$-theories of groups are specified, in which case the concept of centralizer dimension plays an important role.
Keywords: polynilpotent group, free group, variety of metabelian groups, centralizer dimension, $\exists$-theories of groups, $\Phi$-theories of groups. 
@article{AL_2019_58_3_a7,
     author = {E. I. Timoshenko},
     title = {Universal theories and centralizer dimensions of groups},
     journal = {Algebra i logika},
     pages = {397--416},
     publisher = {mathdoc},
     volume = {58},
     number = {3},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2019_58_3_a7/}
}
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E. I. Timoshenko. Universal theories and centralizer dimensions of groups. Algebra i logika, Tome 58 (2019) no. 3, pp. 397-416. http://geodesic.mathdoc.fr/item/AL_2019_58_3_a7/