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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| Datum: | 2025 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Lugansk National Taras Shevchenko University
2025
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| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2351 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| Zusammenfassung: | 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 \(T\) . |
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