Elementary group equivalence with the integral length function

A. G. Myasnikov, V. N. Remeslennikov

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

The paper determines criteria of elementary equivalence for some classes of free groups with operators and free products with the length function. The case of a group with operators admitting rational coordinatizati0n with a finite basis is completely analyzed. They are polycyclic, solvable groups of finite rank without torsion, and Chernikov groups. The concept of t0-isomorphism of groups intermediate between elementary equivalence and isomorphism is important for the aspects of elementary equivalence of groups with operators and free product. It is proved that to-isomorphism of arbitrary groups of operators is followed by the elementary equivalence of the respective free operator groups (free products) with length function.

Original languageEnglish
Pages (from-to)335-354
Number of pages20
JournalIllinois Journal of Mathematics
Volume30
Issue number2
DOIs
StatePublished - 1986

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