{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,24]],"date-time":"2025-02-24T05:25:45Z","timestamp":1740374745861,"version":"3.37.3"},"reference-count":33,"publisher":"World Scientific Pub Co Pte Ltd","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2025,2]]},"abstract":"<jats:p> We prove that the set of subgroups of the automorphism group of a two-sided full shift is closed under countable graph products. We introduce the notion of a group action without A-cancellation (for an abelian group A), and show that when A is a finite abelian group and G is a group of cellular automata whose action does not have A-cancellation, the wreath product [Formula: see text] embeds in the automorphism group of a full shift. We show that all free abelian groups and free groups admit such cellular automata actions. In the one-sided case, we prove variants of these results with reasonable alphabet blow-ups. <\/jats:p>","DOI":"10.1142\/s0218196724500553","type":"journal-article","created":{"date-parts":[[2024,10,25]],"date-time":"2024-10-25T01:01:33Z","timestamp":1729818093000},"page":"49-79","source":"Crossref","is-referenced-by-count":0,"title":["Graph and wreath products of cellular automata"],"prefix":"10.1142","volume":"35","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2059-194X","authenticated-orcid":false,"given":"Ville","family":"Salo","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, University of Turku, Finland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2024,12,7]]},"reference":[{"key":"S0218196724500553BIB002","doi-asserted-by":"publisher","DOI":"10.1515\/crelle-2013-0062"},{"key":"S0218196724500553BIB003","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-39300-1_5"},{"volume-title":"Notes on Infinite Permutation Groups","year":"2006","author":"Bhattacharjee M.","key":"S0218196724500553BIB004"},{"key":"S0218196724500553BIB005","doi-asserted-by":"publisher","DOI":"10.1017\/S0143385700005678"},{"key":"S0218196724500553BIB006","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1988-0927684-2"},{"key":"S0218196724500553BIB007","doi-asserted-by":"publisher","DOI":"10.1007\/BF01445101"},{"key":"S0218196724500553BIB008","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-1019-1_4"},{"key":"S0218196724500553BIB009","doi-asserted-by":"publisher","DOI":"10.1007\/BF02698916"},{"key":"S0218196724500553BIB010","doi-asserted-by":"publisher","DOI":"10.1017\/S0013091500019660"},{"key":"S0218196724500553BIB011","first-page":"28","author":"Coven E. M.","year":"2016","journal-title":"Discrete Anal."},{"key":"S0218196724500553BIB012","doi-asserted-by":"publisher","DOI":"10.3934\/jmd.2018015"},{"key":"S0218196724500553BIB013","doi-asserted-by":"publisher","DOI":"10.3934\/jmd.2016.10.483"},{"key":"S0218196724500553BIB014","doi-asserted-by":"publisher","DOI":"10.1090\/proc12719"},{"key":"S0218196724500553BIB015","doi-asserted-by":"publisher","DOI":"10.1515\/9781400845941"},{"key":"S0218196724500553BIB016","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-4049(99)00175-9"},{"key":"S0218196724500553BIB017","doi-asserted-by":"publisher","DOI":"10.1017\/etds.2015.70"},{"key":"S0218196724500553BIB018","volume":"19","author":"Donoso S.","year":"2017","journal-title":"Discrete Anal."},{"key":"S0218196724500553BIB020","doi-asserted-by":"publisher","DOI":"10.1017\/etds.2017.72"},{"key":"S0218196724500553BIB022","doi-asserted-by":"publisher","DOI":"10.1093\/imrn\/rnab204"},{"key":"S0218196724500553BIB023","doi-asserted-by":"publisher","DOI":"10.1007\/BF01691062"},{"issue":"4","key":"S0218196724500553BIB024","first-page":"203","volume":"1","author":"Kim K. H.","year":"1990","journal-title":"Pure Math. Appl."},{"key":"S0218196724500553BIB025","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511626302"},{"key":"S0218196724500553BIB026","series-title":"Classics in Mathematics","volume-title":"Combinatorial Group Theory","author":"Lyndon R. C.","year":"2015"},{"key":"S0218196724500553BIB027","doi-asserted-by":"publisher","DOI":"10.4171\/ggd\/497"},{"key":"S0218196724500553BIB028","first-page":"1103","volume":"119","author":"Miha\u012dlova K. \u00c3.","year":"1958","journal-title":"Dokl. Akad. Nauk SSSR"},{"issue":"9","key":"S0218196724500553BIB029","first-page":"4173","volume":"33","author":"Olli J.","year":"2013","journal-title":"Dynam. Syst."},{"key":"S0218196724500553BIB030","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196701000401"},{"key":"S0218196724500553BIB031","doi-asserted-by":"publisher","DOI":"10.4064\/cm6463-2-2016"},{"key":"S0218196724500553BIB032","doi-asserted-by":"publisher","DOI":"10.1017\/etds.2016.95"},{"key":"S0218196724500553BIB034","doi-asserted-by":"publisher","DOI":"10.4171\/ggd\/529"},{"key":"S0218196724500553BIB035","doi-asserted-by":"publisher","DOI":"10.4064\/sm190212-18-10"},{"key":"S0218196724500553BIB037","doi-asserted-by":"publisher","DOI":"10.1017\/etds.2014.29"},{"key":"S0218196724500553BIB038","doi-asserted-by":"publisher","DOI":"10.2307\/3597195"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196724500553","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,2,24]],"date-time":"2025-02-24T03:37:27Z","timestamp":1740368247000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S0218196724500553"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,12,7]]},"references-count":33,"journal-issue":{"issue":"01","published-print":{"date-parts":[[2025,2]]}},"alternative-id":["10.1142\/S0218196724500553"],"URL":"https:\/\/doi.org\/10.1142\/s0218196724500553","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"type":"print","value":"0218-1967"},{"type":"electronic","value":"1793-6500"}],"subject":[],"published":{"date-parts":[[2024,12,7]]}}}