{"title":"局部有限\\(p\\) -群的格通用性","authors":"Vladimir B. Repnitskiǐ","doi":"10.15826/umj.2023.1.011","DOIUrl":null,"url":null,"abstract":"For an arbitrary prime \\(p\\), we prove that every algebraic lattice is isomorphic to a complete sublattice in the subgroup lattice of a suitable locally finite \\(p\\)-group. In particular, every lattice is embeddable in the subgroup lattice of a locally finite \\(p\\)-group.","PeriodicalId":36805,"journal":{"name":"Ural Mathematical Journal","volume":"52 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"LATTICE UNIVERSALITY OF LOCALLY FINITE \\\\(p\\\\)-GROUPS\",\"authors\":\"Vladimir B. Repnitskiǐ\",\"doi\":\"10.15826/umj.2023.1.011\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"For an arbitrary prime \\\\(p\\\\), we prove that every algebraic lattice is isomorphic to a complete sublattice in the subgroup lattice of a suitable locally finite \\\\(p\\\\)-group. In particular, every lattice is embeddable in the subgroup lattice of a locally finite \\\\(p\\\\)-group.\",\"PeriodicalId\":36805,\"journal\":{\"name\":\"Ural Mathematical Journal\",\"volume\":\"52 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-07-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Ural Mathematical Journal\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.15826/umj.2023.1.011\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Ural Mathematical Journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.15826/umj.2023.1.011","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
LATTICE UNIVERSALITY OF LOCALLY FINITE \(p\)-GROUPS
For an arbitrary prime \(p\), we prove that every algebraic lattice is isomorphic to a complete sublattice in the subgroup lattice of a suitable locally finite \(p\)-group. In particular, every lattice is embeddable in the subgroup lattice of a locally finite \(p\)-group.
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