We give a complete description of Abelian groups that are totally P-stable for the following four natural types of subgroups: arbitrary subgroups, pure subgroups, elementary subsystems, and algebraically closed subgroups.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
E. A. Palyutin, “P-stable Abelian groups,” Algebra and Logic, 52, No. 5, 404-421 (2013).
E. A. Palyutin, “P-spectra of Abelian groups,” Algebra and Logic, 53, No. 2, 140-165 (2014).
L. Fuchs, Infinite Abelian Groups, Vol. 1, Academic Press, New York (1970).
Yu. L. Ershov and E. A. Palyutin, Mathematical Logic [in Russian], 6th edn., Fizmatlit, Moscow (2011).
W. Hodges, Model Theory, Enc. Math. Appl., 42, Cambridge Univ. Press, Cambridge (1993).
W. Szmielew, “Elementary properties of Abelian groups,” Fund. Math., 41, 203-271 (1955).
E. A. Palyutin, “E∗-stable theories,” Algebra and Logic, 42, No. 2, 112-120 (2003).
M. Ziegler, “Model theory of modules,” Ann. Pure Appl. Log., 26, No. 2, 149-213 (1984).
Author information
Authors and Affiliations
Corresponding author
Additional information
*Supported by KN MON RK, project No. 0830/GF4.
Translated from Algebra i Logika, Vol. 54, No. 4, pp. 463-492, July-August, 2015.
Rights and permissions
About this article
Cite this article
Palyutin, E.A. Totally P-Stable Abelian Groups. Algebra Logic 54, 296–315 (2015). https://doi.org/10.1007/s10469-015-9350-9
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10469-015-9350-9