{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,8,24]],"date-time":"2023-08-24T04:17:29Z","timestamp":1692850649831},"reference-count":18,"publisher":"World Scientific Pub Co Pte Ltd","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2017,6]]},"abstract":"<jats:p>We define a new invariant of a conjugacy class of subgroups which we call the breadth and prove that a quasiconvex subgroup of a negatively curved group has finite breadth in the ambient group. Utilizing the coset graph and the geodesic core of a subgroup we give an explicit algorithm for constructing a finite generating set for an intersection of a quasiconvex subgroup of a negatively curved group with its conjugate. Using that algorithm we construct algorithms for computing the breadth, the width, and the height of a quasiconvex subgroup of a negatively curved group. These algorithms decide if a quasiconvex subgroup of a negatively curved group is almost malnormal in the ambient group. We also explicitly compute a quasiconvexity constant of the intersection of two quasiconvex subgroups and give examples demonstrating that height, width, and breadth are different invariants of a subgroup.<\/jats:p>","DOI":"10.1142\/s0218196717500217","type":"journal-article","created":{"date-parts":[[2017,5,29]],"date-time":"2017-05-29T09:26:21Z","timestamp":1496049981000},"page":"403-419","source":"Crossref","is-referenced-by-count":1,"title":["On intersections of conjugate subgroups"],"prefix":"10.1142","volume":"27","author":[{"given":"Rita","family":"Gitik","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, USA"}]}],"member":"219","published-online":{"date-parts":[[2017,5,29]]},"reference":[{"key":"S0218196717500217BIB001","doi-asserted-by":"crossref","first-page":"1045","DOI":"10.4171\/dm\/421","volume":"18","author":"Agol I.","year":"2013","journal-title":"Doc. Math."},{"key":"S0218196717500217BIB002","doi-asserted-by":"publisher","DOI":"10.1023\/A:1012040207144"},{"key":"S0218196717500217BIB003","doi-asserted-by":"publisher","DOI":"10.2140\/gt.2009.13.1043"},{"key":"S0218196717500217BIB004","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196799000382"},{"key":"S0218196717500217BIB005","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196700000236"},{"key":"S0218196717500217BIB007","doi-asserted-by":"publisher","DOI":"10.1007\/BF02772626"},{"key":"S0218196717500217BIB008","doi-asserted-by":"publisher","DOI":"10.1007\/BF00739330"},{"key":"S0218196717500217BIB009","doi-asserted-by":"publisher","DOI":"10.1007\/s00039-011-0120-0"},{"key":"S0218196717500217BIB011","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511600609.006"},{"key":"S0218196717500217BIB012","first-page":"577","volume":"68","author":"Farb B.","year":"1994","journal-title":"Proc. LMS"},{"key":"S0218196717500217BIB014","doi-asserted-by":"publisher","DOI":"10.1016\/0022-4049(96)00148-X"},{"key":"S0218196717500217BIB015","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-4049(96)00020-5"},{"issue":"5","key":"S0218196717500217BIB016","first-page":"8","volume":"12","author":"Gitik R.","journal-title":"IOSR J. Math."},{"key":"S0218196717500217BIB018","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-98-01792-9"},{"key":"S0218196717500217BIB019","doi-asserted-by":"publisher","DOI":"10.2140\/gt.2009.13.1945"},{"key":"S0218196717500217BIB020","doi-asserted-by":"publisher","DOI":"10.1090\/dimacs\/025\/07"},{"key":"S0218196717500217BIB021","doi-asserted-by":"publisher","DOI":"10.1090\/dimacs\/025\/10"},{"key":"S0218196717500217BIB022","doi-asserted-by":"publisher","DOI":"10.1007\/BF02095993"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196717500217","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,8,23]],"date-time":"2023-08-23T19:50:42Z","timestamp":1692820242000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196717500217"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,5,29]]},"references-count":18,"journal-issue":{"issue":"04","published-online":{"date-parts":[[2017,5]]},"published-print":{"date-parts":[[2017,6]]}},"alternative-id":["10.1142\/S0218196717500217"],"URL":"https:\/\/doi.org\/10.1142\/s0218196717500217","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,5,29]]}}}