This article is cited 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.

MSC: 20F05, 20F06

Received: 09.12.2002

Language: English

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