{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:13:26Z","timestamp":1760058806403,"version":"build-2065373602"},"reference-count":22,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2025,4,27]],"date-time":"2025-04-27T00:00:00Z","timestamp":1745712000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Consider the modular group PSL(2,Z)=\u27e8x,y|x2=y3=1\u27e9 generated by the transformations x:z\u21a6\u22121\/z and y:z\u21a6(z\u22121)\/z. Let H be the proper subgroup \u27e8y,v|y3=v3=1\u27e9 of PSL(2,Z), where v=xyx. For a positive square-free integer n, this article studies the action of H on the subset {a+\u2212nc|a,b=a2+nc,c\u2208Z,c\u22600} of the imaginary quadratic number field Q(\u2212n) where, in particular, the accurate estimate of the number of orbits arising from this action is given, correcting the estimate given in some of the relevant literature.<\/jats:p>","DOI":"10.3390\/axioms14050335","type":"journal-article","created":{"date-parts":[[2025,4,28]],"date-time":"2025-04-28T09:39:47Z","timestamp":1745833187000},"page":"335","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On the Action of a Subgroup of the Modular Group on Imaginary Quadratic Number Fields"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0630-1280","authenticated-orcid":false,"given":"Abdulaziz","family":"Deajim","sequence":"first","affiliation":[{"name":"Department of Mathematics, King Khalid University, Abha 61413, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2025,4,27]]},"reference":[{"key":"ref_1","first-page":"159","article-title":"Coset diagrams and relations for PSL(2,Z)","volume":"1","author":"Higman","year":"1983","journal-title":"Arab Gulf J. 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Available online: https:\/\/math.gsu.edu.tr\/uludag\/kunming.pdf."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/5\/335\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T17:22:41Z","timestamp":1760030561000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/5\/335"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,4,27]]},"references-count":22,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2025,5]]}},"alternative-id":["axioms14050335"],"URL":"https:\/\/doi.org\/10.3390\/axioms14050335","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2025,4,27]]}}}