This article is cited in 8 papers

$P$-stable Abelian groups

E. A. Palyutin<sup>ab

a</sup> Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russia
^b Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090, Russia

Abstract: $(P,a)$-stable and $(P,s)$-stable Abelian groups are described. It is also proved that every Abelian group is $(P,p)$-stable. In particular, results due to M. A. Rusaleev [Algebra Logika, 50, No. 2, 231–245 (2011)] and T. A. Nurmagambetov [Proc. 11th Conf. Math. Logic, Kazan State Univ., Kazan (1992), p. 106] derive from these.

Keywords: $(P,a)$-stable Abelian group, $(P,s)$-stable Abelian group.

UDC: 510.67+512.57

Received: 24.10.2012

 English version: Algebra and Logic, 2013, 52:5, 404–421

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