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Algebra Logika, 2019, Volume 58, Number 3, Pages 344–362 (Mi al899)  

Canonical and algebraically closed groups in universal classes of Abelian groups

A. A. Mishchenko, V. N. Remeslennikov, A. V. Treyer

Omsk Branch of Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: Using sets of finitely generated Abelian groups closed under the discrimination operator, we describe principal universal classes ${\mathcal{K}}$ within a quasivariety ${\mathfrak{A}}_p$, the class of groups whose periodic part is a $p$-group for a prime $p$. Also the concept of an algebraically closed group in ${\mathcal{K}}$ is introduced, and such groups are classified.

Keywords: Abelian group, universal class, principal universal class, canonical group, discriminability of classes of groups, ${\mathcal{K}}$-algebraically closed groups, ladder vector.

Funding Agency Grant Number
Russian Science Foundation 18-71-10028
*Supported by Russian Science Foundation, project No. 18-71-10028.


DOI: https://doi.org/10.33048/alglog.2019.58.304

Full text: PDF file (262 kB)
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English version:
Algebra and Logic, 2019, 58:3, 232–243

Bibliographic databases:

UDC: 512.54.01
Received: 26.08.2017
Revised: 24.09.2019

Citation: A. A. Mishchenko, V. N. Remeslennikov, A. V. Treyer, “Canonical and algebraically closed groups in universal classes of Abelian groups”, Algebra Logika, 58:3 (2019), 344–362; Algebra and Logic, 58:3 (2019), 232–243

Citation in format AMSBIB
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\paper Canonical and algebraically closed groups in universal
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\jour Algebra Logika
\yr 2019
\vol 58
\issue 3
\pages 344--362
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\crossref{https://doi.org/10.33048/alglog.2019.58.304}
\transl
\jour Algebra and Logic
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\vol 58
\issue 3
\pages 232--243
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