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 ∃- and Φ-theories of groups are specified, in which case the concept of centralizer dimension plays an important role.
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E. I. Timoshenko Supported by RFBR, project No. 18-01-00100.
Translated from Algebra i Logika, Vol. 58, No. 3, pp. 397-416, May-June, 2019.
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Timoshenko, E.I. Universal Theories and Centralizer Dimensions of Groups. Algebra Logic 58, 268–281 (2019). https://doi.org/10.1007/s10469-019-09545-z
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DOI: https://doi.org/10.1007/s10469-019-09545-z