Geodesic
Group Quasivarieties with Infinitely Many Maximal Subquasivarieties
Algebra i logika, Tome 41 (2002) no. 1, pp. 3-14

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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. 
@article{AL_2002_41_1_a0,
     author = {V. V. Bludov},
     title = {Group {Quasivarieties} with {Infinitely} {Many} {Maximal} {Subquasivarieties}},
     journal = {Algebra i logika},
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     publisher = {mathdoc},
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     number = {1},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2002_41_1_a0/}
}
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V. V. Bludov. Group Quasivarieties with Infinitely Many Maximal Subquasivarieties. Algebra i logika, Tome 41 (2002) no. 1, pp. 3-14. http://geodesic.mathdoc.fr/item/AL_2002_41_1_a0/