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A criterion for the elementary equivalence of endomorphism rings and automorphism groups of Abelian \(p\)-groups. (English. Russian original) Zbl 1306.20038

Dokl. Math. 90, No. 1, 399-400 (2014); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 457, No. 1, 11-12 (2014).
From the text: We generalize results of Bunina and Roizner on automorphism groups and of Bunina and Mikhalev on endomorphism rings and obtain a criterion for the elementary equivalence of automorphism groups and endomorphism rings of Abelian \(p\)-groups in terms of a second order equivalence of these groups themselves.

MSC:

20F28 Automorphism groups of groups
03C60 Model-theoretic algebra
03C85 Second- and higher-order model theory
20K10 Torsion groups, primary groups and generalized primary groups
20K30 Automorphisms, homomorphisms, endomorphisms, etc. for abelian groups
20A15 Applications of logic to group theory
16S50 Endomorphism rings; matrix rings
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References:

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