Group Quasivarieties with Infinitely Many Maximal Subquasivarieties

V. V. Bludov

Institute of System Dynamics and Control Theory, Siberian Branch of the Russian Academy of Sciences

Abstract: We construct an example of a 2-generated group $G$ and describe a set of proper maximal subquasivarieties in the quasivariety $qG$. This set proves to be infinite, which gives an affirmative answer to Question 14.25 posed by A. I. Budkin in the “Kourovka Notebook”. Moreover, it is shown that every proper subquasivariety in $qG$ is contained in a proper maximal one.

Keywords: group quasivariety, maximal subquasivariety, 2-generated group.

UDC: 512.54

Received: 25.07.2000

 English version: Algebra and Logic, 2002, 41:1, 1–7

Bibliographic databases:

• 
• 
•