Quasi-identities of finite nilpotent groups
Copyright policy )Quasi-identities of finite nilpotent groups
The main theorem of this paper claims the existence of a quasi-identity \(\Phi\) which is true in the free nilpotent class 2 group \(F_2 ({\mathcal N}_2)\) of rank 2, but false in any non-abelian group with no subgroup isomorphic to \(F_2 ({\mathcal N}_2)\), thus giving a negative answer to the question as to whether the quasivariety of torsion-free groups in the quasivariety generated by an infinite set of groups of order the cube of some prime coincides with the quasivariety generated by \(F_2 ({\mathcal N}_2)\). Unfortunately, the reviewer found the proof of one of the main lemmata (Lemma 4) extremely difficult to follow.
- Altai State University Russian Federation
quasivarieties of torsion-free groups, Finite nilpotent groups, \(p\)-groups, Nilpotent groups, quasi-identities, Quasivarieties, free nilpotent class 2 groups, Quasivarieties and varieties of groups
quasivarieties of torsion-free groups, Finite nilpotent groups, \(p\)-groups, Nilpotent groups, quasi-identities, Quasivarieties, free nilpotent class 2 groups, Quasivarieties and varieties of groups
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