{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,14]],"date-time":"2025-05-14T02:28:24Z","timestamp":1747189704472,"version":"3.40.5"},"reference-count":54,"publisher":"World Scientific Pub Co Pte Ltd","issue":"08","funder":[{"name":"Marie Sklodowska-Curie","award":["945322"],"award-info":[{"award-number":["945322"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2023,12]]},"abstract":"<jats:p> For any finite group A and any finitely generated group B, we prove that the corresponding lamplighter group [Formula: see text] admits a standard generating set with unbounded depth, and that if B is abelian then the above is true for every standard generating set. This generalizes the case where [Formula: see text] together with its cyclic generator [S.\u00a0Cleary and J.\u00a0Taback, Dead end words in lamplighter groups and other wreath products, Q.\u00a0J.\u00a0Math.\u00a056(2) (2005) 165\u2013178]. When [Formula: see text] is the free product of two finite groups H and K, we characterize which standard generators of the associated lamplighter group have unbounded depth in terms of a geometrical constant related to the Cayley graphs of H and K. In particular, we find differences with the one-dimensional case: the lamplighter group over the free product of two sufficiently large finite cyclic groups has uniformly bounded depth with respect to some standard generating set. <\/jats:p>","DOI":"10.1142\/s0218196723500571","type":"journal-article","created":{"date-parts":[[2023,8,12]],"date-time":"2023-08-12T03:18:41Z","timestamp":1691810321000},"page":"1489-1530","source":"Crossref","is-referenced-by-count":1,"title":["Dead ends on wreath products and lamplighter groups"],"prefix":"10.1142","volume":"33","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7609-6457","authenticated-orcid":false,"given":"Eduardo","family":"Silva","sequence":"first","affiliation":[{"name":"D\u00e9partement de Math\u00e9matiques et Applications, \u00c9cole Normale Sup\u00e9rieure, 45 rue d\u2019Ulm, F-75230 Paris Cedex 05, France"}]}],"member":"219","published-online":{"date-parts":[[2023,9,13]]},"reference":[{"key":"S0218196723500571BIB001","doi-asserted-by":"publisher","DOI":"10.26493\/1855-3974.509.d9d"},{"key":"S0218196723500571BIB002","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(94)00077-V"},{"key":"S0218196723500571BIB003","doi-asserted-by":"publisher","DOI":"10.1006\/eujc.2001.0456"},{"key":"S0218196723500571BIB004","doi-asserted-by":"publisher","DOI":"10.1002\/net.20126"},{"key":"S0218196723500571BIB005","doi-asserted-by":"publisher","DOI":"10.1142\/S1793525321500096"},{"key":"S0218196723500571BIB006","doi-asserted-by":"publisher","DOI":"10.1007\/s00454-020-00184-1"},{"key":"S0218196723500571BIB007","doi-asserted-by":"publisher","DOI":"10.1007\/BF02671613"},{"key":"S0218196723500571BIB008","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-01978-5"},{"key":"S0218196723500571BIB009","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-349-03521-2"},{"issue":"2","key":"S0218196723500571BIB010","first-page":"190","volume":"26","author":"Brieussel J.","year":"2018","journal-title":"Algebra Discrete Math."},{"key":"S0218196723500571BIB011","doi-asserted-by":"publisher","DOI":"10.2969\/jmsj\/06731213"},{"key":"S0218196723500571BIB012","doi-asserted-by":"publisher","DOI":"10.1006\/aima.1995.1067"},{"key":"S0218196723500571BIB013","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(74)90075-6"},{"key":"S0218196723500571BIB014","series-title":"Textbooks in Mathematics","volume-title":"Graphs & Digraphs","author":"Chartrand G.","year":"2016","edition":"6"},{"key":"S0218196723500571BIB015","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0091805"},{"key":"S0218196723500571BIB016","doi-asserted-by":"publisher","DOI":"10.1515\/9781400885398"},{"key":"S0218196723500571BIB017","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2005.11.016"},{"key":"S0218196723500571BIB018","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-05-08043-3"},{"key":"S0218196723500571BIB019","doi-asserted-by":"publisher","DOI":"10.1093\/qmath\/hah030"},{"key":"S0218196723500571BIB020","doi-asserted-by":"publisher","DOI":"10.1090\/conm\/372\/06886"},{"key":"S0218196723500571BIB021","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(95)00072-5"},{"key":"S0218196723500571BIB022","doi-asserted-by":"publisher","DOI":"10.1016\/j.jpaa.2011.04.018"},{"key":"S0218196723500571BIB023","series-title":"Chicago Lectures in Mathematics","volume-title":"Topics in Geometric Group Theory","author":"de la Harpe P.","year":"2000"},{"key":"S0218196723500571BIB024","doi-asserted-by":"publisher","DOI":"10.26493\/1855-3974.420.3c5"},{"key":"S0218196723500571BIB025","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(74)90090-2"},{"key":"S0218196723500571BIB026","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(74)90091-4"},{"key":"S0218196723500571BIB027","doi-asserted-by":"publisher","DOI":"10.1016\/j.aim.2008.09.014"},{"key":"S0218196723500571BIB028","doi-asserted-by":"publisher","DOI":"10.1002\/mana.19780820120"},{"key":"S0218196723500571BIB029","doi-asserted-by":"publisher","DOI":"10.1137\/0211056"},{"key":"S0218196723500571BIB030","doi-asserted-by":"publisher","DOI":"10.4153\/CMB-1968-037-0"},{"key":"S0218196723500571BIB031","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196711006789"},{"key":"S0218196723500571BIB034","doi-asserted-by":"publisher","DOI":"10.1142\/S1793830919300029"},{"key":"S0218196723500571BIB035","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196709005238"},{"key":"S0218196723500571BIB036","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-61896-3"},{"key":"S0218196723500571BIB037","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(83)90269-8"},{"key":"S0218196723500571BIB038","doi-asserted-by":"publisher","DOI":"10.37236\/7009"},{"key":"S0218196723500571BIB039","doi-asserted-by":"publisher","DOI":"10.1017\/S0305004100033946"},{"key":"S0218196723500571BIB040","first-page":"32","volume":"1","author":"Nekrashevych V.","year":"1998","journal-title":"Dopov. 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