FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2010, VOLUME 16, NUMBER 7, PAGES 181-196

Typical equivalence of linear groups and other algebraic systems

A. D. Maksimov

Abstract

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The paper is devoted to the notion of typical equivalence introduced by B. I. Plotkin. We give some examples of elementarily equivalent objects that are not typically equivalent and show two ways to construct nonisomorphic typically equivalent algebras. We also prove A. I. Maltsev's theorem on elementary equivalence of linear groups over fields for the case of typical equivalence.

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Last modified: October 21, 2011