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Algebra Logika, 2019, Volume 58, Number 3, Pages 397–416 (Mi al903)  

Universal theories and centralizer dimensions of groups

E. I. Timoshenko

Novosibirsk State Technical University

Abstract: 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.

Funding Agency Grant Number
Russian Foundation for Basic Research 18-01-00100_а


DOI: https://doi.org/10.33048/alglog.2019.58.308

Full text: PDF file (262 kB)
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UDC: 512.5
Received: 10.03.2018
Revised: 24.09.2019

Citation: E. I. Timoshenko, “Universal theories and centralizer dimensions of groups”, Algebra Logika, 58:3 (2019), 397–416

Citation in format AMSBIB
\Bibitem{Tim19}
\by E.~I.~Timoshenko
\paper Universal theories and centralizer dimensions of groups
\jour Algebra Logika
\yr 2019
\vol 58
\issue 3
\pages 397--416
\mathnet{http://mi.mathnet.ru/al903}
\crossref{https://doi.org/10.33048/alglog.2019.58.308}


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