On intersections of normal subgroups in groups

• Date: 2018
• Main Author: Kulikova, O. V.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: Normal closure of sets of elements in groups; presentations of groups; pictures; mutual commutants; intersection of groups; aspherisity; 20F05
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1009
• Journal Title: Algebra and Discrete Mathematics

The paper is a generalization of [2]. For a group \(H=\langle A|O\rangle\), conditions for the equality \(\bar N_1\cap \bar N_2 = [\bar N_1,\bar N_2]\) are given in terms of pictures, where \(\bar N_i\) is the normal closure of a set \(\bar R_i\subset H\) for \(i=1,2\).