September 2007 Describing groups
André Nies
Bull. Symbolic Logic 13(3): 305-339 (September 2007). DOI: 10.2178/bsl/1186666149

Abstract

Two ways of describing a group are considered. 1. A group is finite-automaton presentable if its elements can be represented by strings over a finite alphabet, in such a way that the set of representing strings and the group operation can be recognized by finite automata. 2. An infinite f.g. group is quasi-finitely axiomatizable if there is a description consisting of a single first-order sentence, together with the information that the group is finitely generated. In the first part of the paper we survey examples of FA-presentable groups, but also discuss theorems restricting this class. In the second part, we give examples of quasi-finitely axiomatizable groups, consider the algebraic content of the notion, and compare it to the notion of a group which is a prime model. We also show that if a structure is bi-interpretable in parameters with the ring of integers, then it is prime and quasi-finitely axiomatizable.

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André Nies. "Describing groups." Bull. Symbolic Logic 13 (3) 305 - 339, September 2007. https://doi.org/10.2178/bsl/1186666149

Information

Published: September 2007
First available in Project Euclid: 9 August 2007

zbMATH: 1167.20017
MathSciNet: MR2359909
Digital Object Identifier: 10.2178/bsl/1186666149

Rights: Copyright © 2007 Association for Symbolic Logic

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Vol.13 • No. 3 • September 2007
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