{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,7,3]],"date-time":"2024-07-03T00:50:50Z","timestamp":1719967850082},"reference-count":6,"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":[[2010,12]]},"abstract":"<jats:p> Let C(T) be a generalized Coxeter group, which has a natural map onto one of the classical Coxeter groups, either B<jats:sub>n<\/jats:sub> or D<jats:sub>n<\/jats:sub>. Let C<jats:sub>Y<\/jats:sub>(T) be a natural quotient of C(T), and if C(T) is simply-laced (which means all the relations between the generators has order 2 or 3), C<jats:sub>Y<\/jats:sub>(T) is a generalized Coxeter group, too. Let A<jats:sub>t,n<\/jats:sub> be a group which contains t Abelian groups generated by n elements. The main result in this paper is that C<jats:sub>Y<\/jats:sub>(T) is isomorphic to A<jats:sub>t,n<\/jats:sub> \u22ca B<jats:sub>n<\/jats:sub> or A<jats:sub>t,n<\/jats:sub> \u22ca D<jats:sub>n<\/jats:sub>, depends on whether the signed graph T contains loops or not, or in other words C(T) is simply-laced or not, and t is the number of the cycles in T. This result extends the results of Rowen, Teicher and Vishne to generalized Coxeter groups which have a natural map onto one of the classical Coxeter groups. <\/jats:p>","DOI":"10.1142\/s0218196710006023","type":"journal-article","created":{"date-parts":[[2010,12,28]],"date-time":"2010-12-28T05:27:42Z","timestamp":1293514062000},"page":"1041-1062","source":"Crossref","is-referenced-by-count":3,"title":["COXETER COVERS OF THE CLASSICAL COXETER GROUPS"],"prefix":"10.1142","volume":"20","author":[{"given":"MEIRAV","family":"AMRAM","sequence":"first","affiliation":[{"name":"Department of Mathematics, Bar-Ilan University, Ramat-Gan 52900, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"ROBERT","family":"SHWARTZ","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Bar-Ilan University, Ramat-Gan 52900, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"MINA","family":"TEICHER","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Bar-Ilan University, Ramat-Gan 52900, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2012,4,30]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1006\/jabr.1994.1059"},{"key":"rf2","volume":"5","author":"Eriksson H.","journal-title":"Electronic J. Combin."},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511623646"},{"key":"rf4","first-page":"171","volume":"10","author":"Margulis G. A.","journal-title":"J. Lie Theory"},{"key":"rf5","first-page":"139","volume":"8","author":"Rowen L.","journal-title":"J. Group Theory"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1007\/s002080050284"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196710006023","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T23:31:58Z","timestamp":1565134318000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196710006023"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,12]]},"references-count":6,"journal-issue":{"issue":"08","published-online":{"date-parts":[[2012,4,30]]},"published-print":{"date-parts":[[2010,12]]}},"alternative-id":["10.1142\/S0218196710006023"],"URL":"https:\/\/doi.org\/10.1142\/s0218196710006023","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,12]]}}}