The algorithms that recognize Milnor laws and properties of these laws

Witold Tomaszewski

Algebra and discrete mathematics, Tome 17 (2014) no. 2, pp. 308-332.

Résumé

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.

Détail

Keywords: group laws, Milnor laws, metabelian groups.

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