P-compatible Abelian groups

Krystyna Mruczek-Nasieniewska

DOI: http://dx.doi.org/10.12775/LLP.2005.016

Abstract


Let τ : F → N be a type of a variety V . Every partition P of the set F determines a so-called P-compatible variety. We consider the varieties GnP defined by so-called P-compatible identities of Abelian groups with exponent n. Besides, we study a connection between the lattice of all partitions of the set F and the lattice of all subvarieties of the variety defined by some kind of P-compatible identities — externally compatible identities satisfied in the class of all Abelian groups with exponent n.



Keywords


Abelian groups; P-compatible identity; variety; partition of a set

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References


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