{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T05:17:06Z","timestamp":1777353426322,"version":"3.51.4"},"reference-count":19,"publisher":"World Scientific Pub Co Pte Lt","issue":"01n02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2002,2]]},"abstract":"<jats:p> We study a torsion free weakly branch group G without free subgroups defined by a three state automaton which appears in different problems related to amenability, Galois groups and monodromy. Here and in the forthcoming paper [20] we establish several important properties of G related to fractalness, branchness, just infinitness, growth, amenability and presentations. <\/jats:p>","DOI":"10.1142\/s0218196702001000","type":"journal-article","created":{"date-parts":[[2002,7,27]],"date-time":"2002-07-27T11:07:52Z","timestamp":1027768072000},"page":"223-246","source":"Crossref","is-referenced-by-count":66,"title":["ON A TORSION-FREE WEAKLY BRANCH GROUP DEFINED BY A THREE STATE AUTOMATON"],"prefix":"10.1142","volume":"12","author":[{"given":"ROSTISLAV I.","family":"GRIGORCHUK","sequence":"first","affiliation":[{"name":"Steklov Mathematical Institute,  Gubkina Str. 8 Moscow, 117966, Russia"}]},{"given":"ANDRZEJ","family":"\u017bUK","sequence":"additional","affiliation":[{"name":"CNRS, Ecole Normale Sup\u00e9rieure de Lyon, Unit\u00e9 de Math\u00e9matiques Pures et Appliqu\u00e9es, 46,  All\u00e9e d'Italie, F-69364 Lyon Cedex 07, France"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"p_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0764-4442(00)01658-X"},{"key":"p_3","doi-asserted-by":"publisher","DOI":"10.1016\/S0764-4442(01)01946-2"},{"key":"p_5","doi-asserted-by":"publisher","DOI":"10.1006\/jabr.1998.7579"},{"issue":"2","key":"p_6","first-page":"3","volume":"42","author":"Cannon J. W.","year":"1996","journal-title":"Enseign. Math."},{"issue":"3","key":"p_7","doi-asserted-by":"crossref","first-page":"396","DOI":"10.1215\/ijm\/1256047608","volume":"24","author":"Chou C.","year":"1980","journal-title":"Illinois J. Math."},{"key":"p_8","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1215\/ijm\/1255380675","volume":"1","author":"Day M.","year":"1957","journal-title":"Illinois J. Math."},{"key":"p_9","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1984-0743744-X"},{"key":"p_11","first-page":"16","author":"Greenleaf F. P.","year":"1969","journal-title":"Van Nostrand Mathematical Studies"},{"issue":"1","key":"p_13","first-page":"30","volume":"271","author":"Grigorchuk R. I.","year":"1983","journal-title":"Dokl. Akad. Nauk SSSR"},{"issue":"5","key":"p_14","first-page":"939","volume":"48","author":"Grigorchuk R. I.","year":"1984","journal-title":"Izv. Akad. Nauk SSSR Ser. Mat."},{"issue":"3","key":"p_15","first-page":"305","volume":"43","author":"Grigorchuk R. I.","year":"1998","journal-title":"Matem. Zamet."},{"key":"p_16","doi-asserted-by":"publisher","DOI":"10.4213\/sm293"},{"key":"p_17","first-page":"75","author":"Grigorchuk R. I.","year":"2000","journal-title":"Birkh\u00e4user"},{"key":"p_21","doi-asserted-by":"publisher","DOI":"10.1007\/BF02471762"},{"key":"p_23","first-page":"134","volume":"231","author":"Grigorchuk R. I.","year":"2000","journal-title":"Proc. Steklov Inst. Math."},{"key":"p_24","doi-asserted-by":"publisher","DOI":"10.1007\/BF01179757"},{"key":"p_26","doi-asserted-by":"crossref","first-page":"146","DOI":"10.7146\/math.scand.a-10568","volume":"7","author":"Kesten H.","year":"1959","journal-title":"Math. Scand."},{"issue":"4","key":"p_27","first-page":"503","volume":"38","author":"Lysionok I. G.","year":"1985","journal-title":"Mat. Zametki"},{"issue":"4","key":"p_29","first-page":"199","volume":"35","author":"Olshanskii A.","year":"1980","journal-title":"Uspekhi Mat. Nauk"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196702001000","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T21:58:30Z","timestamp":1565128710000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196702001000"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,2]]},"references-count":19,"journal-issue":{"issue":"01n02","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2002,2]]}},"alternative-id":["10.1142\/S0218196702001000"],"URL":"https:\/\/doi.org\/10.1142\/s0218196702001000","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2002,2]]}}}