This article is cited in 5 papers

Recursive $p$-adic numbers and elementary theories of finitely generated pro-$p$-groups

A. G. Myasnikov, V. N. Remeslennikov


Abstract: The authors propose a method of effective presentation of finitely generated pro-$p$-groups, and use it to study the elementary theories of such groups. They prove that elementarily equivalent finitely generated pro-$p$-groups are isomorphic. The main result is the following criterion: the elementary theory of a finitely generated nilpotent pro-$p$-group $G$ is decidable if and only if $G$ is effectively presented.
Bibliography: 18 titles.

UDC: 519.45

MSC: Primary 20E18, 20F50; Secondary 20A15

Received: 07.02.1985

 English version: Mathematics of the USSR-Izvestiya, 1988, 30:3, 577–597

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