Geodesic
The algorithms that recognize Milnor laws and properties of these laws
Algebra and discrete mathematics, Tome 17 (2014) no. 2, pp. 308-332

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We consider several equivalent definitions of the so-called Milnor laws (or Milnor identities) that is the laws which are not satisfied in $\mathfrak{A}_p\mathfrak{A}$ varieties. The purpose of this article is to provide algorithms that allow us to check whether a given identity $w(x,y)$ has one of the following properties: $w(x,y)$ is a Milnor law, every nilpotent group satisfying $w(x,y)$ is abelian, every finitely generated metabelian group satisfying $w(x,y)$ is finite-by-abelian.
Keywords: group laws, Milnor laws, metabelian groups. 
@article{ADM_2014_17_2_a10,
     author = {Witold Tomaszewski},
     title = {The algorithms that recognize {Milnor} laws and properties of these laws},
     journal = {Algebra and discrete mathematics},
     pages = {308--332},
     publisher = {mathdoc},
     volume = {17},
     number = {2},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2014_17_2_a10/}
}
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Witold Tomaszewski. The algorithms that recognize Milnor laws and properties of these laws. Algebra and discrete mathematics, Tome 17 (2014) no. 2, pp. 308-332. http://geodesic.mathdoc.fr/item/ADM_2014_17_2_a10/