Note on quasivarieties generated by finite pointed abelian groups

Abstract

We prove that a finite pointed abelian group generates a finitely axiomatizable variety that has a finite quasivariety lattice. As a consequence, we obtain that a quasivariety generated by a finite pointed abelian group has a finite basis of quasi-identities. The problems arising from the results obtained are also discussed.

Keywords

• variety
• quasivariety
• quasivariety lattice
• finitely axiomatizable class
• abelian group
• pointed group
• 06b20
• 08b05
• 08c15
• 20n99