{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,14]],"date-time":"2025-05-14T02:28:27Z","timestamp":1747189707379,"version":"3.40.5"},"reference-count":20,"publisher":"World Scientific Pub Co Pte Ltd","issue":"04","funder":[{"name":"Spanish Government Project","award":["PID2020-117281GB-I00"],"award-info":[{"award-number":["PID2020-117281GB-I00"]}]},{"name":"Basque Government Project","award":["IT483-22"],"award-info":[{"award-number":["IT483-22"]}]},{"name":"Marie Sklodowska-Curie Grant Agreement","award":["101067088"],"award-info":[{"award-number":["101067088"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2024,6]]},"abstract":"<jats:p> The subgroup lattice of a group is a great source of information about the structure of the group itself. The aim of this paper is to use a similar tool for studying profinite groups. In more detail, we study the lattices of closed or open subgroups of a profinite group and its relation with the whole group. We show, for example, that procyclic groups are the only profinite groups with a distributive lattice of closed or open subgroups, and we give a sharp characterization of profinite groups whose lattice of closed (or open) subgroups satisfies the Dedekind modular law; we actually give a precise description of the behavior of modular elements of the lattice of closed subgroups. We also deal with the problem of carrying some structural information from a profinite group to another one having an isomorphic lattice of closed (or open) subgroups. Some interesting consequences and related results concerning decomposability and the number of profinite groups with a given lattice of closed (or open) subgroups are also obtained. <\/jats:p>","DOI":"10.1142\/s0218196724500206","type":"journal-article","created":{"date-parts":[[2024,4,11]],"date-time":"2024-04-11T10:16:10Z","timestamp":1712830570000},"page":"515-542","source":"Crossref","is-referenced-by-count":0,"title":["On the lattice of closed subgroups of a profinite group"],"prefix":"10.1142","volume":"34","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7506-0652","authenticated-orcid":false,"given":"Francesco","family":"de Giovanni","sequence":"first","affiliation":[{"name":"Dipartimento di Matematica e Applicazioni \u201cRenato Caccioppoli\u201d, Universit\u00e0 degli Studi di Napoli Federico II, Complesso Universitario Monte S.\u00a0Angelo, Via Cintia, Napoli, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0275-1417","authenticated-orcid":false,"given":"Iker","family":"de las Heras","sequence":"additional","affiliation":[{"name":"Zientzia eta Teknologia Fakultatea, Matematika Departamentua, Euskal Herriko Unibertsitatea, Sarriena Auzoa z\/g, Leioa, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4532-3690","authenticated-orcid":false,"given":"Marco","family":"Trombetti","sequence":"additional","affiliation":[{"name":"Dipartimento di Matematica e Applicazioni \u201cRenato Caccioppoli\u201d, Universit\u00e0 degli Studi di Napoli Federico II, Complesso Universitario Monte S.\u00a0Angelo, Via Cintia, Napoli, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2024,5,9]]},"reference":[{"key":"S0218196724500206BIB001","doi-asserted-by":"publisher","DOI":"10.1007\/s00209-021-02955-9"},{"key":"S0218196724500206BIB002","doi-asserted-by":"publisher","DOI":"10.4153\/S0008439522000418"},{"key":"S0218196724500206BIB003","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-61703-4"},{"key":"S0218196724500206BIB004","doi-asserted-by":"publisher","DOI":"10.1007\/BF01193620"},{"key":"S0218196724500206BIB005","doi-asserted-by":"publisher","DOI":"10.1007\/s00013-018-1190-0"},{"key":"S0218196724500206BIB006","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511470882"},{"key":"S0218196724500206BIB007","doi-asserted-by":"publisher","DOI":"10.1007\/s11856-022-2404-5"},{"key":"S0218196724500206BIB008","doi-asserted-by":"publisher","DOI":"10.1007\/s11856-021-2267-1"},{"key":"S0218196724500206BIB009","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2016.11.028"},{"key":"S0218196724500206BIB010","doi-asserted-by":"publisher","DOI":"10.1515\/JGT.2007.035"},{"key":"S0218196724500206BIB011","doi-asserted-by":"publisher","DOI":"10.1016\/S1631-073X(03)00349-2"},{"key":"S0218196724500206BIB012","doi-asserted-by":"publisher","DOI":"10.1215\/S0012-7094-38-00419-3"},{"key":"S0218196724500206BIB013","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-04097-3"},{"key":"S0218196724500206BIB014","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-07241-7"},{"key":"S0218196724500206BIB015","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4684-0128-8"},{"key":"S0218196724500206BIB016","doi-asserted-by":"publisher","DOI":"10.1007\/BF01181188"},{"key":"S0218196724500206BIB017","doi-asserted-by":"publisher","DOI":"10.1515\/9783110868647"},{"key":"S0218196724500206BIB018","doi-asserted-by":"publisher","DOI":"10.1007\/s00013-023-01851-4"},{"key":"S0218196724500206BIB019","first-page":"317","volume":"69","author":"Zacher G.","year":"1980","journal-title":"Atti Accad. 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