{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,19]],"date-time":"2025-03-19T11:14:36Z","timestamp":1742382876145},"reference-count":51,"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":[[2018,12]]},"abstract":"<jats:p> We extend Borel\u2019s theorem on the dominance of word maps from semisimple algebraic groups to some perfect groups. In another direction, we generalize Borel\u2019s theorem to some words with constants. We also consider the surjectivity problem for particular words and groups, give a brief survey of recent results, present some generalizations and variations and discuss various approaches, with emphasis on new ideas, constructions and connections. <\/jats:p>","DOI":"10.1142\/s0218196718400052","type":"journal-article","created":{"date-parts":[[2018,7,26]],"date-time":"2018-07-26T02:35:31Z","timestamp":1532572531000},"page":"1487-1515","source":"Crossref","is-referenced-by-count":13,"title":["Word maps on perfect algebraic groups"],"prefix":"10.1142","volume":"28","author":[{"given":"Nikolai","family":"Gordeev","sequence":"first","affiliation":[{"name":"Department of Mathematics, Herzen State Pedagogical University, 48 Moika Embankment, 191186, St. Petersburg, Russia"},{"name":"Department of Mathematics of Sankt-Petersburg State University, 198504, Universitetsky Prospekt, 28, Peterhof, St. Petersburg, Russia"}]},{"given":"Boris","family":"Kunyavski\u012d","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Bar-Ilan University, 5290002 Ramat Gan, Israel"}]},{"given":"Eugene","family":"Plotkin","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Bar-Ilan University, 5290002 Ramat Gan, Israel"}]}],"member":"219","published-online":{"date-parts":[[2019,1,14]]},"reference":[{"key":"S0218196718400052BIB001","doi-asserted-by":"publisher","DOI":"10.1112\/blms\/bdt063"},{"key":"S0218196718400052BIB002","doi-asserted-by":"publisher","DOI":"10.4171\/GGD\/162"},{"key":"S0218196718400052BIB003","first-page":"175","volume":"12","author":"Bandman T.","year":"2014","journal-title":"Cent. Eur. J. Math."},{"key":"S0218196718400052BIB004","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2012.01.012"},{"key":"S0218196718400052BIB005","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2013.02.031"},{"key":"S0218196718400052BIB006","doi-asserted-by":"publisher","DOI":"10.1007\/s40879-016-0101-9"},{"key":"S0218196718400052BIB007","doi-asserted-by":"publisher","DOI":"10.1007\/s00013-017-1130-4"},{"key":"S0218196718400052BIB008","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1994-1254833-X"},{"key":"S0218196718400052BIB009","first-page":"151","volume":"29","author":"Borel A.","year":"1983","journal-title":"Enseign. Math."},{"key":"S0218196718400052BIB010","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0941-6"},{"key":"S0218196718400052BIB011","series-title":"Chaps. IV, V, VI","volume-title":"\u00c9l\u00e9ments de Math\u00e9matiques: Groupes et Alg\u00e8bres de Lie","author":"Bourbaki N.","year":"1981","edition":"2"},{"key":"S0218196718400052BIB012","doi-asserted-by":"publisher","DOI":"10.1006\/jabr.2001.9007"},{"key":"S0218196718400052BIB013","doi-asserted-by":"publisher","DOI":"10.4310\/MRL.2002.v9.n6.a4"},{"key":"S0218196718400052BIB014","doi-asserted-by":"publisher","DOI":"10.4310\/MRL.2003.v10.n5.a6"},{"key":"S0218196718400052BIB015","series-title":"Panoramas et Synth\u00e8ses 42\/43","first-page":"93","volume-title":"Autour des sch\u00e9mas en groupes","author":"Conrad B.","year":"2014"},{"key":"S0218196718400052BIB016","doi-asserted-by":"publisher","DOI":"10.1515\/jgth-2017-0013"},{"key":"S0218196718400052BIB017","doi-asserted-by":"publisher","DOI":"10.1512\/iumj.2014.63.5391"},{"key":"S0218196718400052BIB018","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-98-01953-9"},{"key":"S0218196718400052BIB019","doi-asserted-by":"publisher","DOI":"10.2140\/pjm.2004.214.245"},{"key":"S0218196718400052BIB022","doi-asserted-by":"publisher","DOI":"10.1006\/jabr.1995.1111"},{"key":"S0218196718400052BIB025","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2014.10.045"},{"key":"S0218196718400052BIB027","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2017.03.016"},{"key":"S0218196718400052BIB029","doi-asserted-by":"publisher","DOI":"10.2969\/jmsj\/00130270"},{"key":"S0218196718400052BIB030","series-title":"Lecture Notes Pure and Applied Mathematics","volume-title":"Semisimple Lie Algebras","volume":"38","author":"Goto M.","year":"1978"},{"key":"S0218196718400052BIB031","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-8114-3"},{"key":"S0218196718400052BIB033","doi-asserted-by":"publisher","DOI":"10.1007\/s11856-015-1246-9"},{"key":"S0218196718400052BIB034","doi-asserted-by":"publisher","DOI":"10.1080\/00029890.1977.11994465"},{"key":"S0218196718400052BIB035","doi-asserted-by":"publisher","DOI":"10.3103\/S1063454113010044"},{"key":"S0218196718400052BIB036","doi-asserted-by":"publisher","DOI":"10.2140\/agt.2017.17.331"},{"key":"S0218196718400052BIB037","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781316106877.016"},{"key":"S0218196718400052BIB038","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2011.10.040"},{"key":"S0218196718400052BIB039","doi-asserted-by":"publisher","DOI":"10.1093\/imrn\/rns109"},{"key":"S0218196718400052BIB041","doi-asserted-by":"publisher","DOI":"10.4171\/JEMS\/220"},{"key":"S0218196718400052BIB042","doi-asserted-by":"publisher","DOI":"10.1112\/blms\/bdr043"},{"issue":"336","key":"S0218196718400052BIB043","first-page":"xi+117","volume":"58","author":"Lubotzky A.","year":"1985","journal-title":"Mem. Amer. Math. Soc."},{"key":"S0218196718400052BIB044","first-page":"325","volume":"361","author":"Malle G.","year":"2014","journal-title":"Ast\u00e9risque"},{"key":"S0218196718400052BIB045","doi-asserted-by":"publisher","DOI":"10.1007\/s00031-010-9111-8"},{"key":"S0218196718400052BIB046","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2013.08.030"},{"key":"S0218196718400052BIB047","doi-asserted-by":"publisher","DOI":"10.2307\/2372490"},{"key":"S0218196718400052BIB048","doi-asserted-by":"publisher","DOI":"10.1112\/S0024609303002601"},{"key":"S0218196718400052BIB049","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1951-0040298-4"},{"key":"S0218196718400052BIB050","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1962-0169947-4"},{"key":"S0218196718400052BIB051","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1964-0161944-X"},{"key":"S0218196718400052BIB052","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139107082"},{"key":"S0218196718400052BIB053","doi-asserted-by":"publisher","DOI":"10.4007\/annals.2009.170.1383"},{"key":"S0218196718400052BIB054","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-39286-3_22"},{"key":"S0218196718400052BIB055","doi-asserted-by":"publisher","DOI":"10.1080\/00927870903366843"},{"key":"S0218196718400052BIB057","doi-asserted-by":"publisher","DOI":"10.4310\/MRL.2003.v10.n5.a5"},{"key":"S0218196718400052BIB058","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2010.06.015"},{"key":"S0218196718400052BIB059","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2012.04.007"},{"key":"S0218196718400052BIB060","doi-asserted-by":"publisher","DOI":"10.4153\/CMB-2011-155-3"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196718400052","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T21:41:18Z","timestamp":1565127678000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196718400052"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,12]]},"references-count":51,"journal-issue":{"issue":"08","published-online":{"date-parts":[[2019,1,14]]},"published-print":{"date-parts":[[2018,12]]}},"alternative-id":["10.1142\/S0218196718400052"],"URL":"https:\/\/doi.org\/10.1142\/s0218196718400052","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,12]]}}}