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Algebra and Discrete Mathematics, 2003, Issue 1, Pages 36–67
(Mi adm368)
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This article is cited in 3 scientific papers (total in 3 papers)
RESEARCH ARTICLE
On intersections of normal subgroups in free groups
O. V. Kulikova Department of Mechanics and Mathematics, Moscow State
University,Vorobievy Gory 1, 119992 Moscow,
Russia
Abstract:
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.
Keywords:
normal closure of words in free groups, presentations of groups, pictures, mutual commutants, intersection of groups, aspherisity, small cancellation conditions.
Received: 09.12.2002
Citation:
O. V. Kulikova, “On intersections of normal subgroups in free groups”, Algebra Discrete Math., 2003, no. 1, 36–67
Linking options:
https://www.mathnet.ru/eng/adm368 https://www.mathnet.ru/eng/adm/y2003/i1/p36
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Abstract page: | 135 | Full-text PDF : | 106 | First page: | 1 |
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