On finite state automaton actions of HNN extensions of free abelian groups
HNN extensions of free abelian groups are considered. For arbitrary prime $p$ it is introduced a class of such extensions that act by finite automaton permutations over an alphabet $ \mathsf{X} $ of cardinality $p$ and belong to $p$-Sylow subgroup of the group of automaton permutations over such $ \...
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| Format: | Article |
| Language: | English |
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Vasyl Stefanyk Precarpathian National University
2021-06-01
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| Series: | Karpatsʹkì Matematičnì Publìkacìï |
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| Online Access: | https://journals.pnu.edu.ua/index.php/cmp/article/view/5000 |
| _version_ | 1797205791907774464 |
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| author | V. Prokhorchuk |
| author_facet | V. Prokhorchuk |
| author_sort | V. Prokhorchuk |
| collection | DOAJ |
| description | HNN extensions of free abelian groups are considered. For arbitrary prime $p$ it is introduced a class of such extensions that act by finite automaton permutations over an alphabet $ \mathsf{X} $ of cardinality $p$ and belong to $p$-Sylow subgroup of the group of automaton permutations over such $ \mathsf{X} $. As a corollary it implies that all corresponding HNN extensions are residually $p$-finite. |
| first_indexed | 2024-04-24T08:56:45Z |
| format | Article |
| id | doaj.art-752fb242aa9b40f3bc2d3dd60d4a2298 |
| institution | Directory Open Access Journal |
| issn | 2075-9827 2313-0210 |
| language | English |
| last_indexed | 2024-04-24T08:56:45Z |
| publishDate | 2021-06-01 |
| publisher | Vasyl Stefanyk Precarpathian National University |
| record_format | Article |
| series | Karpatsʹkì Matematičnì Publìkacìï |
| spelling | doaj.art-752fb242aa9b40f3bc2d3dd60d4a22982024-04-16T07:05:54ZengVasyl Stefanyk Precarpathian National UniversityKarpatsʹkì Matematičnì Publìkacìï2075-98272313-02102021-06-0113118018810.15330/cmp.13.1.180-1884344On finite state automaton actions of HNN extensions of free abelian groupsV. Prokhorchuk0https://orcid.org/0000-0001-5203-9239Taras Shevchenko National University of Kyiv, 64/13 Volodymyrska str., 01601, Kyiv, UkraineHNN extensions of free abelian groups are considered. For arbitrary prime $p$ it is introduced a class of such extensions that act by finite automaton permutations over an alphabet $ \mathsf{X} $ of cardinality $p$ and belong to $p$-Sylow subgroup of the group of automaton permutations over such $ \mathsf{X} $. As a corollary it implies that all corresponding HNN extensions are residually $p$-finite.https://journals.pnu.edu.ua/index.php/cmp/article/view/5000automaton groupautomorphism of rooted treehnn extension |
| spellingShingle | V. Prokhorchuk On finite state automaton actions of HNN extensions of free abelian groups Karpatsʹkì Matematičnì Publìkacìï automaton group automorphism of rooted tree hnn extension |
| title | On finite state automaton actions of HNN extensions of free abelian groups |
| title_full | On finite state automaton actions of HNN extensions of free abelian groups |
| title_fullStr | On finite state automaton actions of HNN extensions of free abelian groups |
| title_full_unstemmed | On finite state automaton actions of HNN extensions of free abelian groups |
| title_short | On finite state automaton actions of HNN extensions of free abelian groups |
| title_sort | on finite state automaton actions of hnn extensions of free abelian groups |
| topic | automaton group automorphism of rooted tree hnn extension |
| url | https://journals.pnu.edu.ua/index.php/cmp/article/view/5000 |
| work_keys_str_mv | AT vprokhorchuk onfinitestateautomatonactionsofhnnextensionsoffreeabeliangroups |