{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,9,26]],"date-time":"2023-09-26T05:56:08Z","timestamp":1695707768247},"reference-count":11,"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":[[2003,2]]},"abstract":"<jats:p> In this note we give simple explicit examples of free subgroups of rank 2 in the group of infinite upper unitriangular matrices over integers. The proofs that the given subgroup is free are elementary. Using canonical projections mod p (p \u2014 any odd prime) we obtain also free subgroups in the group of finite state automata on alphabet of size p, extending results of Aleshin [1], Brunner\u2013Sidki [2] and Olijnyk\u2013Sushchansky [8, 9] in this direction. As application, we give the simple proofs of two classical results on free groups. <\/jats:p>","DOI":"10.1142\/s0218196703001341","type":"journal-article","created":{"date-parts":[[2003,3,27]],"date-time":"2003-03-27T09:28:57Z","timestamp":1048757337000},"page":"81-86","source":"Crossref","is-referenced-by-count":7,"title":["FREE SUBGROUPS OF THE GROUP OF INFINITE UNITRIANGULAR MATRICES"],"prefix":"10.1142","volume":"13","author":[{"given":"WALDEMAR","family":"HO\u0141UBOWSKI","sequence":"first","affiliation":[{"name":"Institute of Mathematics, Silesian University  of Technology, Kaszubska 23, 44-101 Gliwice, Poland"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","first-page":"10","volume":"38","author":"Aleshin S. V.","journal-title":"Moscow Univ. Math. Bull."},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196798000077"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1112\/blms\/22.3.222"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8693(71)90107-4"},{"key":"rf5","first-page":"136","volume":"4","author":"Levi F. W.","journal-title":"J. Indian Math. Soc."},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1007\/BF01472217"},{"key":"rf7","volume-title":"Combinatorial Group Theory","author":"Magnus W.","year":"1966"},{"key":"rf8","first-page":"158","volume":"14","author":"Olijnyk A.","journal-title":"Voprosy algebry \u2014 Gomel"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1007\/BF02676668"},{"key":"rf10","first-page":"657","volume":"57","author":"Sanov I. N.","journal-title":"Doklady Akad. Nauk SSSR (N. S.)"},{"key":"rf11","volume-title":"The Banach\u2013Tarski paradox","author":"Wagon S.","year":"1993"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196703001341","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T21:56:45Z","timestamp":1565128605000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196703001341"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,2]]},"references-count":11,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2003,2]]}},"alternative-id":["10.1142\/S0218196703001341"],"URL":"https:\/\/doi.org\/10.1142\/s0218196703001341","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2003,2]]}}}