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...
Gespeichert in:
| Datum: | 2018 |
|---|---|
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Lugansk National Taras Shevchenko University
2018
|
| Schlagworte: | |
| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/952 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Algebra and Discrete Mathematics |
Institution
Algebra and Discrete Mathematics| Zusammenfassung: | 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. |
|---|