Coverings in the lattice of quasivarieties of groups
Copyright policy )Coverings in the lattice of quasivarieties of groups
Let P be an infinite set of odd primes and M(P) the quasivariety of groups defined by quasi-identities \([x,y^ i,x]=1\to [x,y^ j,x]=1\) where i,j\(\in P\). Then M(P) has continuum covers in the lattice \(L_ q\) of quasivarieties of groups. There exist continuum quasivarieties of groups Q which have continuum covers in \(L_ q\) and satisfy any of the following conditions: (i) Q is not a variety; (ii) Q contains free groups; (iii) Q consists of torsion-free groups; (iv) Q lies in the variety \(N_ 2A\) and has continuum covers in \(N_ 2A\).
coverings in the lattice of quasivarieties of groups, Lattices of varieties, quasi-identities, quasivariety of groups, Quasivarieties, Quasivarieties and varieties of groups, covers in the lattice of quasivarieties, quasi- identities
coverings in the lattice of quasivarieties of groups, Lattices of varieties, quasi-identities, quasivariety of groups, Quasivarieties, Quasivarieties and varieties of groups, covers in the lattice of quasivarieties, quasi- identities
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