Describing Groups

Show simple item record Nies, Andre en 2011-11-30T19:07:34Z en 2007 en
dc.identifier.citation Bulletin of Symbolic Logic 13:305-339 2007 en
dc.identifier.issn 1079-8986 en
dc.identifier.uri en
dc.description.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. en
dc.publisher Association for Symbolic Logic en
dc.relation.ispartofseries Bulletin of Symbolic Logic en
dc.rights Items in ResearchSpace are protected by copyright, with all rights reserved, unless otherwise indicated. Previously published items are made available in accordance with the copyright policy of the publisher. en
dc.rights.uri en
dc.title Describing Groups en
dc.type Journal Article en
dc.identifier.doi 10.2178/bsl/1186666149 en
pubs.begin-page 305 en
pubs.volume 13 en
dc.rights.holder Copyright: Association for Symbolic Logic en en
pubs.end-page 339 en
dc.rights.accessrights en
pubs.subtype Article en
pubs.elements-id 76433 en Science en School of Computer Science en
pubs.record-created-at-source-date 2010-09-01 en

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