{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,3]],"date-time":"2022-04-03T11:47:15Z","timestamp":1648986435147},"reference-count":22,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2012,5]]},"abstract":"<jats:p> We prove that for any finite index subgroup \u0393 in SL <jats:sub>n<\/jats:sub>(\u2124), there exists k = k(n) \u2208 \u2115, \u03f5 = \u03f5(\u0393) &gt; 0, and an infinite family of finite index subgroups in \u0393 with a Kazhdan constant greater than \u03f5 with respect to a generating set of order k. On the other hand, we prove that for any finite index subgroup \u0393 of SL <jats:sub>n<\/jats:sub>(\u2124), and for any \u03f5 &gt; 0 and k \u2208 \u2115, there exists a finite index subgroup \u0393\u2032 \u2264 \u0393 such that the Kazhdan constant of any finite index subgroup in \u0393\u2032 is less than \u03f5, with respect to any generating set of order k. In addition, we prove that the Kazhdan constant of the principal congruence subgroup \u0393<jats:sub>n<\/jats:sub>(m), with respect to a generating set consisting of elementary matrices (and their conjugates), is greater than [Formula: see text], where c &gt; 0 depends only on n. For a fixed n, this bound is asymptotically best possible. <\/jats:p>","DOI":"10.1142\/s0218196712500269","type":"journal-article","created":{"date-parts":[[2012,1,18]],"date-time":"2012-01-18T08:39:47Z","timestamp":1326875987000},"page":"1250026","source":"Crossref","is-referenced-by-count":0,"title":["ON KAZHDAN CONSTANTS OF FINITE INDEX SUBGROUPS IN <font>SL<\/font><sub>n<\/sub>(\u2124)"],"prefix":"10.1142","volume":"22","author":[{"given":"UZY","family":"HADAD","sequence":"first","affiliation":[{"name":"Department of Mathematics, Weizmann Institute of Science, Rehovot 76100, Israel"},{"name":"Computer Science Division, The Open University of Israel, Raanana 43107, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2012,5,6]]},"reference":[{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9904-1964-11107-1"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511542749"},{"key":"rf4","first-page":"36","volume":"413","author":"Burger M.","journal-title":"J. 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