{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,9,28]],"date-time":"2023-09-28T12:19:04Z","timestamp":1695903544240},"reference-count":28,"publisher":"World Scientific Pub Co Pte Ltd","issue":"06","funder":[{"name":"NRF","award":["2018R1D1A1B07043291"],"award-info":[{"award-number":["2018R1D1A1B07043291"]}]},{"name":"NRF","award":["2018R1D1A1B07043268"],"award-info":[{"award-number":["2018R1D1A1B07043268"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2023,9]]},"abstract":"<jats:p> The action of a right-angled Artin group on its extension graph is known to be acylindrical because the cardinality of the so-called r-quasi-stabilizer of a pair of distant points is bounded above by a function of r. The known upper bound of the cardinality is an exponential function of r. In this paper we show that the r-quasi-stabilizer is a subset of a cyclic group and its cardinality is bounded above by a linear function of r. This is done by exploring lattice theoretic properties of group elements, studying prefixes of powers and extending the uniqueness of quasi-roots from word length to star length. We also improve the known lower bound for the minimal asymptotic translation length of a right-angled Artin group on its extension graph. <\/jats:p>","DOI":"10.1142\/s021819672350056x","type":"journal-article","created":{"date-parts":[[2023,7,20]],"date-time":"2023-07-20T01:48:25Z","timestamp":1689817705000},"page":"1217-1267","source":"Crossref","is-referenced-by-count":0,"title":["Acylindricity of the action of right-angled Artin groups on extension graphs"],"prefix":"10.1142","volume":"33","author":[{"given":"Eon-Kyung","family":"Lee","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, Sejong University, Seoul, Korea"}]},{"given":"Sang-Jin","family":"Lee","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Konkuk University, Seoul, Korea"}]}],"member":"219","published-online":{"date-parts":[[2023,8,7]]},"reference":[{"issue":"1","key":"S021819672350056XBIB002","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1007\/s10711-022-00736-0","volume":"217","author":"Baik H.","year":"2023","journal-title":"Geom. 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