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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.
DOI:
https://doi.org/10.33048/alglog.2019.58.308
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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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http://mi.mathnet.ru/eng/al903 http://mi.mathnet.ru/eng/al/v58/i3/p397
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