{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,2]],"date-time":"2026-03-02T08:05:46Z","timestamp":1772438746510,"version":"3.50.1"},"reference-count":8,"publisher":"World Scientific Pub Co Pte Lt","issue":"08","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2011,12]]},"abstract":"<jats:p>In [Todor Tsankov, The additive group of the rationals does not have an automatic presentation, May 2009, arXiv:0905.1505v1], it was shown that the group of rational numbers is not FA-presentable, i.e. it does not admit a presentation by a finite automaton. More generally, any torsion-free abelian group that is divisible by infinitely many primes is not of this kind. In this article we extend the result from [13] and prove that any torsion-free FA-presentable abelian group G is an extension of a finite rank free group by a finite direct sum of Pr\u00fcfer groups \u2124(p<jats:sup>\u221e<\/jats:sup>).<\/jats:p>","DOI":"10.1142\/s0218196711006625","type":"journal-article","created":{"date-parts":[[2011,5,16]],"date-time":"2011-05-16T02:24:07Z","timestamp":1305512647000},"page":"1463-1472","source":"Crossref","is-referenced-by-count":12,"title":["BREAKING UP FINITE AUTOMATA PRESENTABLE TORSION-FREE ABELIAN GROUPS"],"prefix":"10.1142","volume":"21","author":[{"given":"G\u00c1BOR","family":"BRAUN","sequence":"first","affiliation":[{"name":"Alfr\u00e9d R\u00e9nyi Institute of Mathematics, Budapest, Re\u00e1ltanoda u. 13\u201315, 1053, Hungary"}]},{"given":"LUTZ","family":"STR\u00dcNGMANN","sequence":"additional","affiliation":[{"name":"Fakult\u00e4t f\u00fcr Mathematik, Universit\u00e4t Duisburg\u2013Essen, Campus Essen, 45117 Essen, Germany"}]}],"member":"219","published-online":{"date-parts":[[2012,4,5]]},"reference":[{"key":"rf2","series-title":"Pure and Applied Mathematics","volume-title":"Infinite Abelian Groups","volume":"36","author":"L\u00e1szl\u00f3 Fuchs","year":"1970"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(82)90042-1"},{"key":"rf6","first-page":"181","volume":"94","author":"Khoussainov B.","journal-title":"Bull. Eur. Assoc. Theoret. Comput. Sci., EATCS"},{"key":"rf7","first-page":"18","volume":"3","author":"Khoussainov B.","journal-title":"Log. Meth. Comput. Sci."},{"key":"rf8","series-title":"Algebra Logic and Application","doi-asserted-by":"crossref","DOI":"10.1201\/9781482287486","volume-title":"Almost Completely Decomposable Groups","volume":"13","author":"Mader A.","year":"2000"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-72734-7_29"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2007.04.015"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511755149"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196711006625","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,6,19]],"date-time":"2020-06-19T04:38:09Z","timestamp":1592541489000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196711006625"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,12]]},"references-count":8,"journal-issue":{"issue":"08","published-online":{"date-parts":[[2012,4,5]]},"published-print":{"date-parts":[[2011,12]]}},"alternative-id":["10.1142\/S0218196711006625"],"URL":"https:\/\/doi.org\/10.1142\/s0218196711006625","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,12]]}}}