Finitely generated subgroups of branch groups and subdirect products of just infinite groups
| Autor: | Rostislav Grigorchuk, Paul-Henry Leemann, Tatiana Nagnibeda |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Statement (computer science)
20E07 20E08 20E28 General Mathematics 010102 general mathematics Structure (category theory) Block (permutation group theory) Group Theory (math.GR) Grigorchuk group 01 natural sciences Separable space Combinatorics Mathematics::Group Theory Corollary 0103 physical sciences FOS: Mathematics 010307 mathematical physics Finitely-generated abelian group 0101 mathematics Mathematics - Group Theory Mathematics |
| Zdroj: | Izvestiya: Mathematics. 85:1128-1145 |
| ISSN: | 1064-5632 |
| Popis: | The aim of this paper is to describe the structure of the finitely generated subgroups of a family of branch groups, which includes the first Grigorchuk group and the Gupta-Sidki 3-group. This description is made via the notion of block subgroup. We then use this to show that all groups in the above family are subgroup separable (LERF). These results are obtained as a corollary of a more general structural statement on subdirect products of just infinite groups. 22 pages, 2 figures; V3: Final version, to appear in Izvestiya: Mathematics |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|