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Algebra Logika, 2014, Volume 53, Number 2, Pages 216–255 (Mi al632)  

This article is cited in 2 scientific papers (total in 2 papers)

$P$-spectra of Abelian groups

E. A. Palyutinab

a Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russia
b Novosibirsk State Universitys, ul. Pirogova 2, Novosibirsk, 630090, Russia

Abstract: We consider four types of subgroups of Abelian groups: arbitrary subgroups ($s$-subgroups), algebraically closed subgroups ($a$-subgroups), pure subgroups ($p$-subgroups), and elementary subgroups ($e$-subgroups). A language $L(X)$ is an extension of a language $L$ by a set $X$ of constants. A language $L_P$ is an extension of $L$ by one unary predicate symbol $P$. For $i\in\{s,a,p,e\}$ let $\Delta_i$ consist of sentences in $L_P$ , where $L$ is the language of Abelian groups, expressing the fact that a predicate $P$ defines a subgroup of type $i$. For a complete theory $T$ of Abelian groups and for $i\in\{s,a,p,e\}$, a cardinal function assigning a cardinal $\lambda$ the supremum of the number of completions of sets $(T^*\cup\{P(a)\mid a\in X\}\cup\Delta_i)$ in the language $(L(X))_P$ for complete extensions $T^*$ of $T$ in the language $L(X)$ for sets $X$ of cardinality $\lambda$ is called the $(P,i)$- spectrum of the theory $T$. For each $i\in\{s,a,p,e\}$, we describe all possible $(P,i)$-spectra of complete theories of Abelian groups.

Keywords: Abelian group, complete theory, $P$-spectrum.

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English version:
Algebra and Logic, 2014, 53:2, 140–165

Bibliographic databases:

Document Type: Article
UDC: 510.67+512.57
Received: 19.09.2013

Citation: E. A. Palyutin, “$P$-spectra of Abelian groups”, Algebra Logika, 53:2 (2014), 216–255; Algebra and Logic, 53:2 (2014), 140–165

Citation in format AMSBIB
\Bibitem{Pal14}
\by E.~A.~Palyutin
\paper $P$-spectra of Abelian groups
\jour Algebra Logika
\yr 2014
\vol 53
\issue 2
\pages 216--255
\mathnet{http://mi.mathnet.ru/al632}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3237391}
\transl
\jour Algebra and Logic
\yr 2014
\vol 53
\issue 2
\pages 140--165
\crossref{https://doi.org/10.1007/s10469-014-9278-5}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000339821300006}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84905040837}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. E. A. Palyutin, “Totally $P$-stable Abelian groups”, Algebra and Logic, 54:4 (2015), 296–315  mathnet  crossref  crossref  mathscinet  isi
    2. A. A. Mishchenko, V. N. Remeslennikov, A. V. Treier, “Canonical and existential groups in universal classes of abelian groups”, Dokl. Math., 93:2 (2016), 175–178  crossref  crossref  mathscinet  zmath  isi  elib  elib  scopus
  • Алгебра и логика Algebra and Logic
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