{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,4]],"date-time":"2026-06-04T08:03:51Z","timestamp":1780560231645,"version":"3.54.1"},"reference-count":35,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2014,1,15]],"date-time":"2014-01-15T00:00:00Z","timestamp":1389744000000},"content-version":"unspecified","delay-in-days":2328,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Bull. symb. log."],"published-print":{"date-parts":[[2007,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Two ways of describing a group are considered. 1. A group is<jats:italic>finite-automaton presentable<\/jats:italic>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<jats:italic>quasi-finitely axiomatizable<\/jats:italic>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.<\/jats:p>","DOI":"10.2178\/bsl\/1186666149","type":"journal-article","created":{"date-parts":[[2007,12,13]],"date-time":"2007-12-13T14:56:48Z","timestamp":1197557808000},"page":"305-339","source":"Crossref","is-referenced-by-count":49,"title":["Describing Groups"],"prefix":"10.1017","volume":"13","author":[{"given":"Andr\u00e9","family":"Nies","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2014,1,15]]},"reference":[{"key":"S1079898600002055_ref016","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1090\/trans2\/045\/14","article-title":"On a correspondence between rings and groups","volume":"45","author":"Mal'cev","year":"1965","journal-title":"American Mathematical Society Translations"},{"key":"S1079898600002055_ref001","unstructured":"Akiyama S. , Frougny F. , and Sakharovitch J. , Powers of rationals modulo 1 and rational base systems, preprint, 2005."},{"key":"S1079898600002055_ref029","volume-title":"A course in the theory of groups","author":"Robinson","year":"1988"},{"key":"S1079898600002055_ref017","doi-asserted-by":"publisher","DOI":"10.1112\/S0024610704006106"},{"key":"S1079898600002055_ref009","first-page":"39","article-title":"Th\u00e9ories d\u00e9cidables par automate fini","volume":"7","author":"Hodgson","year":"1983","journal-title":"Annales des Sciences Math\u00e9matiques du Quebec"},{"key":"S1079898600002055_ref022","article-title":"Finite automaton presentable groups and rings","author":"Nies","journal-title":"Journal of Algebra"},{"key":"S1079898600002055_ref008","unstructured":"Hodgson B. 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