Canonical and algebraically closed groups in universal

A. A. Mishchenko ; V. N. Remeslennikov ; A. V. Treyer

Algebra i logika, Tome 58 (2019) no. 3, pp. 344-362.

Résumé

Using sets of finitely generated Abelian groups closed under the discrimination operator, we describe principal universal classes ${\mathcal{K}}$ within a quasivariety ${\mathfrak{A}}_p$, the class of groups whose periodic part is a $p$-group for a prime $p$. Also the concept of an algebraically closed group in ${\mathcal{K}}$ is introduced, and such groups are classified.

Détail

Keywords: Abelian group, universal class, canonical group, discriminability of classes of groups, ${\mathcal{K}}$-algebraically closed groups, ladder vector.
Mots-clés : principal universal class

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