Continual series of minimal quasivarieties of $l$-groups

A continuum of distinct linear orders is defined on the free two-generator group $F_2$. For each of the orders, every nonabelian subgroup contains a subgroup which is order-isomorpliic to the entire linearly ordered group $F_2$. Each of these linearly ordered groups $F_2$ generates a quasi variety of $l$-groups which covers the variety of abelian $l$-groups in the lattice of $l$-quasivarieties.