{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T21:10:59Z","timestamp":1760130659539,"version":"build-2065373602"},"reference-count":29,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2023,8,30]],"date-time":"2023-08-30T00:00:00Z","timestamp":1693353600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Princess Nourah bint Abdulrahman University Researchers","award":["PNURSP2023R87"],"award-info":[{"award-number":["PNURSP2023R87"]}]},{"name":"Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia","award":["PNURSP2023R87"],"award-info":[{"award-number":["PNURSP2023R87"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Symmetries in the context of hypergroups and their generalizations are closely related to the algebraic structures and transformations that preserve certain properties of hypergroup operations. Symmetric LA-hypergroups are indeed commutative hypergroups. This paper considers a category of cyclic hyperstructures called the cyclic LA-semihypergroup that is a conception of LA-semihypergroups and cyclic hypergroups. We inaugurate the idea of cyclic LA-hypergroups. The interconnected notions of single-power cyclic LA-hypergroups, non-single power cyclic LA-hypergroups and some of their properties are explored.<\/jats:p>","DOI":"10.3390\/sym15091668","type":"journal-article","created":{"date-parts":[[2023,8,30]],"date-time":"2023-08-30T09:48:15Z","timestamp":1693388895000},"page":"1668","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On Cyclic LA-Hypergroups"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0009-0003-1188-9255","authenticated-orcid":false,"given":"Shehzadi Salma","family":"Kanwal","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, Riphah International University, Sector I-14, Islamabad 44000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5362-9916","authenticated-orcid":false,"given":"Naveed","family":"Yaqoob","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Riphah International University, Sector I-14, Islamabad 44000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5529-0565","authenticated-orcid":false,"given":"Nabilah","family":"Abughazalah","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, College of Science, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0314-876X","authenticated-orcid":false,"given":"Muhammad","family":"Gulistan","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, University of Alberta, Edmonton, AB T6G 2R3, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,8,30]]},"reference":[{"key":"ref_1","first-page":"41","article-title":"On almost semigroups","volume":"36","author":"Kazim","year":"1977","journal-title":"Port. Math."},{"key":"ref_2","first-page":"57","article-title":"On locally associative LA-semigroups","volume":"19","author":"Mushtaq","year":"1979","journal-title":"J. Nat. Sci. Math."},{"key":"ref_3","first-page":"427","article-title":"Abelian groups defined by LA-semigroups","volume":"18","author":"Mushtaq","year":"1983","journal-title":"Stud. Sci. Math. 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