{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,4,15]],"date-time":"2025-04-15T12:55:38Z","timestamp":1744721738189},"reference-count":10,"publisher":"World Scientific Pub Co Pte Ltd","issue":"08","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2017,12]]},"abstract":"<jats:p>Giving a condition for the amenability of groups, Rosenblatt and Willis first introduced the concept of configuration. From the beginning of the theory, the question whether the concept of configuration equivalence coincides with the concept of group isomorphism was posed. We negatively answer this question by introducing two non-isomorphic, solvable and hence amenable groups which are configuration equivalent. Also, we will prove this conjecture, due to Rosenblatt and Willis, whether the configuration equivalent groups include the free non-Abelian group of the same rank or not. We show that two-sided equivalent groups have same class numbers.<\/jats:p>","DOI":"10.1142\/s0218196717500503","type":"journal-article","created":{"date-parts":[[2017,11,8]],"date-time":"2017-11-08T07:56:19Z","timestamp":1510127779000},"page":"1073-1085","source":"Crossref","is-referenced-by-count":2,"title":["Configuration equivalence is not equivalent to isomorphism"],"prefix":"10.1142","volume":"27","author":[{"given":"Ali","family":"Rejali","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Isfahan, Isfahan, 81746-73441, Iran"}]},{"given":"Meisam Soleimani","family":"Malekan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Isfahan, Isfahan, 81746-73441, Iran"}]}],"member":"219","published-online":{"date-parts":[[2017,12,28]]},"reference":[{"key":"S0218196717500503BIB001","doi-asserted-by":"publisher","DOI":"10.1142\/S0219498809003333"},{"issue":"3","key":"S0218196717500503BIB002","doi-asserted-by":"crossref","first-page":"861","DOI":"10.1215\/ijm\/1258131056","volume":"48","author":"Abdollahi A.","year":"2004","journal-title":"Illinois J. Math."},{"key":"S0218196717500503BIB003","doi-asserted-by":"publisher","DOI":"10.4171\/041"},{"key":"S0218196717500503BIB004","volume-title":"Geometry of Defining Relations in Groups","author":"O\u013ashanskii A. Yu.","year":"2012"},{"key":"S0218196717500503BIB005","doi-asserted-by":"publisher","DOI":"10.4007\/annals.2010.172.1"},{"issue":"2","key":"S0218196717500503BIB006","first-page":"87","volume":"13","author":"Rejali A.","year":"2014","journal-title":"J. Algebra Appl."},{"key":"S0218196717500503BIB007","first-page":"1427","volume":"23","author":"Rejali A.","year":"2017","journal-title":"New York J. Math."},{"key":"S0218196717500503BIB009","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-319-08031-4","volume-title":"Combinatorial Algebra: Syntax and Semantics","author":"Sapir M.","year":"2014"},{"key":"S0218196717500503BIB010","volume-title":"Combinatorial Group Theory: Presentations of Groups in Terms of Generators and Relations","author":"Solitar D.","year":"2004"},{"issue":"1","key":"S0218196717500503BIB011","first-page":"3","volume":"19","author":"Tavakoli A.","year":"2014","journal-title":"Matematika"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196717500503","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,8,28]],"date-time":"2023-08-28T04:33:11Z","timestamp":1693197191000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196717500503"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,12]]},"references-count":10,"journal-issue":{"issue":"08","published-online":{"date-parts":[[2017,12,28]]},"published-print":{"date-parts":[[2017,12]]}},"alternative-id":["10.1142\/S0218196717500503"],"URL":"https:\/\/doi.org\/10.1142\/s0218196717500503","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,12]]}}}