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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
E. I. Timoshenko Supported by RFBR, project No. 18-01-00100.


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

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English version:
Algebra and Logic, 2019, 58:3, 268–281

Bibliographic databases:

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; Algebra and Logic, 58:3 (2019), 268–281

Citation in format AMSBIB
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\issue 3
\pages 397--416
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\vol 58
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\pages 268--281
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  • http://mi.mathnet.ru/eng/al/v58/i3/p397

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