On intersections of normal subgroups in free groups
Algebra and discrete mathematics, no. 1 (2003), pp. 36-67
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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 $$ 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.
Keywords:
normal closure of words in free groups, presentations of groups, pictures, mutual commutants, intersection of groups, aspherisity, small cancellation conditions.
O. V. Kulikova. On intersections of normal subgroups in free groups. Algebra and discrete mathematics, no. 1 (2003), pp. 36-67. http://geodesic.mathdoc.fr/item/ADM_2003_1_a4/
@article{ADM_2003_1_a4,
author = {O. V. Kulikova},
title = {On intersections of normal subgroups in free groups},
journal = {Algebra and discrete mathematics},
pages = {36--67},
year = {2003},
number = {1},
language = {en},
url = {http://geodesic.mathdoc.fr/item/ADM_2003_1_a4/}
}