{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,19]],"date-time":"2025-09-19T11:18:41Z","timestamp":1758280721947},"reference-count":39,"publisher":"World Scientific Pub Co Pte Lt","issue":"06","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2013,9]]},"abstract":"<jats:p> We define the notion of preGarside group slightly lightening the definition of Garside group so that all Artin\u2013Tits groups are preGarside groups. This paper intends to give a first basic study on these groups. Firstly, we introduce the notion of parabolic subgroup, we prove that any preGarside group has a (partial) complemented presentation, and we characterize the parabolic subgroups in terms of these presentations. Afterwards we prove that the amalgamated product of two preGarside groups along a common parabolic subgroup is again a preGarside group. This enables us to define the family of preGarside groups of FC type as the smallest family of preGarside groups that contains the Garside groups and that is closed by amalgamation along parabolic subgroups. Finally, we make an algebraic and combinatorial study on FC type preGarside groups and their parabolic subgroups. <\/jats:p>","DOI":"10.1142\/s021819671350029x","type":"journal-article","created":{"date-parts":[[2013,6,24]],"date-time":"2013-06-24T01:26:52Z","timestamp":1372037212000},"page":"1431-1467","source":"Crossref","is-referenced-by-count":1,"title":["PREGARSIDE MONOIDS AND GROUPS, PARABOLICITY, AMALGAMATION, AND FC PROPERTY"],"prefix":"10.1142","volume":"23","author":[{"given":"EDDY","family":"GODELLE","sequence":"first","affiliation":[{"name":"Laboratoire LMNO, UMR 6139 du CNRS, Universit\u00e9 de Caen, Campus II, 14032 Caen cedex, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"LUIS","family":"PARIS","sequence":"additional","affiliation":[{"name":"Institut de Math\u00e9matiques de Bourgogne, UMR 5584 du CNRS, Universit\u00e9 de Bourgogne, B.P. 47870, 21078 Dijon cedex, France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2013,9,19]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-4049(97)00047-9"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1023\/A:1005216814166"},{"key":"rf3","first-page":"247","volume":"23","author":"Arnol'd V. 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