On intersections of normal subgroups in free groups

• Date: 2018
• Main Author: Kulikova, O. V.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: normal closure of words in free groups; presentations of groups; pictures; mutual commutants; intersection of groups; aspherisity; small cancellation conditions; 20F05; 20F06
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/952
• Journal Title: Algebra and Discrete Mathematics

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...