Geodesic
Faithful Group Actions and Aspherical Complexes
Informatics and Automation, Geometric topology, discrete geometry, and set theory, Tome 252 (2006), pp. 184-193

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For a free group $F$ and normal subgroups $R$ and $S$ of $F$, we study the question of whether the action of the group $F/RS$ on the abelian group $\frac {R\cap S}{[R,S]}$ with respect to conjugation in $F$ is faithful. We find conditions on the subgroups $R$ and $S$ under which this action is faithful and apply this theory to the study of the asphericity of two-dimensional CW-complexes and derived series in groups. One of the applications of the method considered in this paper is a description of obstructions to the asphericity of the so-called LOT presentations in terms of transfinite derived series. 
@article{TRSPY_2006_252_a15,
     author = {R. V. Mikhailov},
     title = {Faithful {Group} {Actions} and {Aspherical} {Complexes}},
     journal = {Informatics and Automation},
     pages = {184--193},
     publisher = {mathdoc},
     volume = {252},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2006_252_a15/}
}
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R. V. Mikhailov. Faithful Group Actions and Aspherical Complexes. Informatics and Automation, Geometric topology, discrete geometry, and set theory, Tome 252 (2006), pp. 184-193. http://geodesic.mathdoc.fr/item/TRSPY_2006_252_a15/