On intersections of normal subgroups in free groups
Let \(N_1\) (respectively \(N_2\)) be a normal closure of a set \(R_1=\{ u_i \}\) (respectively \(R_2=\{ v_j \}\)) of cyclically reduced words of the free group \(F(A)\). In the paper we consider geometric conditions on \(R_1\) and \(R_2\) for \(N_1\cap N_2=[N_1,N_2].\) In particular, it turns out t...
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| Дата: | 2018 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2018
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/952 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543412584448000 |
|---|---|
| author | Kulikova, O. V. |
| author_facet | Kulikova, O. V. |
| author_sort | Kulikova, O. V. |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2018-05-13T06:43:21Z |
| description | Let \(N_1\) (respectively \(N_2\)) be a normal closure of a set \(R_1=\{ u_i \}\) (respectively \(R_2=\{ v_j \}\)) of cyclically reduced words of the free group \(F(A)\). In the paper we consider geometric conditions on \(R_1\) and \(R_2\) for \(N_1\cap N_2=[N_1,N_2].\) In particular, it turns out that if a presentation \(<A\, \mid R_1,R_2>\) is aspherical (for example, it satisfies small cancellation conditions \(C(p)\& T(q)\) with \(1/p+1/q=1/2\)), then the equality \(N_1\cap N_2=[N_1,N_2]\) holds. |
| first_indexed | 2025-12-02T15:43:42Z |
| format | Article |
| id | admjournalluguniveduua-article-952 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:43:42Z |
| publishDate | 2018 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-9522018-05-13T06:43:21Z On intersections of normal subgroups in free groups Kulikova, O. V. normal closure of words in free groups, presentations of groups, pictures, mutual commutants, intersection of groups, aspherisity, small cancellation conditions 20F05, 20F06 Let \(N_1\) (respectively \(N_2\)) be a normal closure of a set \(R_1=\{ u_i \}\) (respectively \(R_2=\{ v_j \}\)) of cyclically reduced words of the free group \(F(A)\). In the paper we consider geometric conditions on \(R_1\) and \(R_2\) for \(N_1\cap N_2=[N_1,N_2].\) In particular, it turns out that if a presentation \(<A\, \mid R_1,R_2>\) is aspherical (for example, it satisfies small cancellation conditions \(C(p)\& T(q)\) with \(1/p+1/q=1/2\)), then the equality \(N_1\cap N_2=[N_1,N_2]\) holds. Lugansk National Taras Shevchenko University 2018-05-13 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/952 Algebra and Discrete Mathematics; Vol 2, No 1 (2003) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/952/481 Copyright (c) 2018 Algebra and Discrete Mathematics |
| spellingShingle | normal closure of words in free groups presentations of groups pictures mutual commutants intersection of groups aspherisity small cancellation conditions 20F05 20F06 Kulikova, O. V. On intersections of normal subgroups in free groups |
| title | On intersections of normal subgroups in free groups |
| title_full | On intersections of normal subgroups in free groups |
| title_fullStr | On intersections of normal subgroups in free groups |
| title_full_unstemmed | On intersections of normal subgroups in free groups |
| title_short | On intersections of normal subgroups in free groups |
| title_sort | on intersections of normal subgroups in free groups |
| topic | normal closure of words in free groups presentations of groups pictures mutual commutants intersection of groups aspherisity small cancellation conditions 20F05 20F06 |
| topic_facet | normal closure of words in free groups presentations of groups pictures mutual commutants intersection of groups aspherisity small cancellation conditions 20F05 20F06 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/952 |
| work_keys_str_mv | AT kulikovaov onintersectionsofnormalsubgroupsinfreegroups |