{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,19]],"date-time":"2026-01-19T00:19:08Z","timestamp":1768781948576,"version":"3.49.0"},"reference-count":4,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[1998,2]]},"abstract":"<jats:p> The linear group GL(n, Z) is residually finite by virtue of its action on the (one-rooted) regular 2<jats:sup>n<\/jats:sup>-ary coset tree for Z<jats:sup>n<\/jats:sup>. In this paper we construct finite state automata which effect this action. This shows that GL(n, Z) is embeddable in the group of finite state automorphisms of the one-rooted regular tree of valency 2<jats:sup>n<\/jats:sup>. <\/jats:p>","DOI":"10.1142\/s0218196798000077","type":"journal-article","created":{"date-parts":[[2003,7,31]],"date-time":"2003-07-31T10:08:41Z","timestamp":1059646121000},"page":"127-139","source":"Crossref","is-referenced-by-count":38,"title":["The Generation of GL(n, Z) by Finite State Automata"],"prefix":"10.1142","volume":"08","author":[{"given":"A. M.","family":"Brunner","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Wisconsin-Parkside, Kenosha, WI 53141-2000, USA"}]},{"given":"Said","family":"Sidki","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica, Universidade de Bras\u00edlia, Bras\u00edlia-DF, 70.910-900, Brazil"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"p_1","first-page":"8","volume":"3","author":"Aleshin S. V.","year":"1983","journal-title":"Mathematica"},{"key":"p_2","doi-asserted-by":"publisher","DOI":"10.1006\/jabr.1995.1053"},{"key":"p_4","first-page":"30","volume":"271","author":"Grigorchuk R. I.","year":"1983","journal-title":"Dokl. Akad. Nauk SSSR"},{"key":"p_5","first-page":"179","volume":"7","author":"Magnus W.","year":"1973","journal-title":"Kl. II"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196798000077","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T21:53:59Z","timestamp":1565128439000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196798000077"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998,2]]},"references-count":4,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[1998,2]]}},"alternative-id":["10.1142\/S0218196798000077"],"URL":"https:\/\/doi.org\/10.1142\/s0218196798000077","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[1998,2]]}}}