Branch actions and the structure lattice
J. S. Wilson proved in 1971 an isomorphism between the structural lattice associated to a group belonging to his second class of groups with every proper quotient finite and the Boolean algebra of clopen subsets of Cantor’s ternary set. In this paper we generalize this isomorphism to the class of br...
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| Мова: | English |
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Lugansk National Taras Shevchenko University
2025
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| Назва журналу: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-23512025-01-19T19:44:59Z Branch actions and the structure lattice Fariña-Asategui, Jorge Grigorchuk, Rostislav branch actions, the structure lattice, Boolean algebras, Stone spaces J. S. Wilson proved in 1971 an isomorphism between the structural lattice associated to a group belonging to his second class of groups with every proper quotient finite and the Boolean algebra of clopen subsets of Cantor’s ternary set. In this paper we generalize this isomorphism to the class of branch groups. Moreover, we show that for every faithful branch action of a group \(G\) on a spherically homogeneous rooted tree \(T\) there is a canonical \(G\)-equivariant isomorphism between the Boolean algebra associated to the structure lattice of \(G\) and the Boolean algebra of clopen subsets of the boundary of \(T\) . Lugansk National Taras Shevchenko University 2025-01-19 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2351 10.12958/adm2351 Algebra and Discrete Mathematics; Vol 38, No 2 (2024): A special issue 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2351/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/2351/1263 Copyright (c) 2025 Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics |
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2025-01-19T19:44:59Z |
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OJS |
| language |
English |
| topic |
branch actions the structure lattice Boolean algebras Stone spaces |
| spellingShingle |
branch actions the structure lattice Boolean algebras Stone spaces Fariña-Asategui, Jorge Grigorchuk, Rostislav Branch actions and the structure lattice |
| topic_facet |
branch actions the structure lattice Boolean algebras Stone spaces |
| format |
Article |
| author |
Fariña-Asategui, Jorge Grigorchuk, Rostislav |
| author_facet |
Fariña-Asategui, Jorge Grigorchuk, Rostislav |
| author_sort |
Fariña-Asategui, Jorge |
| title |
Branch actions and the structure lattice |
| title_short |
Branch actions and the structure lattice |
| title_full |
Branch actions and the structure lattice |
| title_fullStr |
Branch actions and the structure lattice |
| title_full_unstemmed |
Branch actions and the structure lattice |
| title_sort |
branch actions and the structure lattice |
| description |
J. S. Wilson proved in 1971 an isomorphism between the structural lattice associated to a group belonging to his second class of groups with every proper quotient finite and the Boolean algebra of clopen subsets of Cantor’s ternary set. In this paper we generalize this isomorphism to the class of branch groups. Moreover, we show that for every faithful branch action of a group \(G\) on a spherically homogeneous rooted tree \(T\) there is a canonical \(G\)-equivariant isomorphism between the Boolean algebra associated to the structure lattice of \(G\) and the Boolean algebra of clopen subsets of the boundary of \(T\) . |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2025 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2351 |
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AT farinaasateguijorge branchactionsandthestructurelattice AT grigorchukrostislav branchactionsandthestructurelattice |
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2025-01-08T04:02:55Z |
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2025-01-20T04:04:23Z |
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