Geodesic
Using Fox Derivatives in Treating Groups of the Form $F/[R',F]$
Algebra i logika, Tome 45 (2006) no. 1, pp. 114-125

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For a factor group with respect to periodic part of a group of the form $F/[R',F]$, an embedding in the matrix group is defined. The criteria for a matrix to belong to an image of this group and for elements to be conjugate are specified. Some statements having a direct bearing on groups of the form in question are proved. Application of the results obtained allows us to refine the answer in [7] to a question by O. Chapuis concerning the universal classification of $\forall$-free soluble groups with two generators.
Keywords: Fox derivatives, universal theory, Magnus–Kuz'min embedding.
Mots-clés : soluble group 
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     author = {E. I. Timoshenko},
     title = {Using {Fox} {Derivatives} in {Treating} {Groups} of the {Form} $F/[R',F]$},
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     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2006_45_1_a5/}
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E. I. Timoshenko. Using Fox Derivatives in Treating Groups of the Form $F/[R',F]$. Algebra i logika, Tome 45 (2006) no. 1, pp. 114-125. http://geodesic.mathdoc.fr/item/AL_2006_45_1_a5/