This article is cited in 1 paper

A criterion of elementary equivalence of automorphism groups of reduced Abelian $p$-groups

M. A. Roizner

Lomonosov Moscow State University, Moscow, Russia

Abstract: We consider Abelian $p$-groups ($p\geq3$) $A_1$ and $A_2$ with nonzero divisible parts. In this paper, we prove that the automorphism groups $\operatorname{Aut}A_1$ and $\operatorname{Aut}A_2$ are elementarily equivalent if and only if the groups $A_1$ and $A_2$ are equivalent in second-order logic.

UDC: 512.541.6+510.67

 English version: Journal of Mathematical Sciences (New York), 2014, 201:4, 519–526

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