Geodesic
On intersections of normal subgroups in groups
Algebra and discrete mathematics, no. 4 (2004), pp. 32-47 Cet article a éte moissonné depuis la source Math-Net.Ru

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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 $i=1,2$.
Keywords: Normal closure of sets of elements in groups, presentations of groups, pictures, mutual commutants, intersection of groups, aspherisity. 
@article{ADM_2004_4_a2,
     author = {O. V. Kulikova},
     title = {On intersections of normal subgroups in groups},
     journal = {Algebra and discrete mathematics},
     pages = {32--47},
     year = {2004},
     number = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2004_4_a2/}
}
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O. V. Kulikova. On intersections of normal subgroups in groups. Algebra and discrete mathematics, no. 4 (2004), pp. 32-47. http://geodesic.mathdoc.fr/item/ADM_2004_4_a2/