Embedding lattices in lattices of varieties of groups

Autor:	M I Anokhin
Rok vydání:	1999
Předmět:	Subvariety General Mathematics Cartesian product Linear subspace Combinatorics symbols.namesake Complete lattice Lattice (order) symbols Condensed Matter::Strongly Correlated Electrons Isomorphism Variety (universal algebra) Mathematics Vector space
Zdroj:	Izvestiya: Mathematics. 63:649-665
ISSN:	1468-4810 1064-5632
DOI:	10.1070/im1999v063n04abeh000250
Popis:	If? is a?variety of groups and? is a?subvariety, then the symbol denotes the complete lattice of varieties? such that . Let , where? is the lattice of subspaces of the -dimensional vector space over the field of two elements, and let be the Cartesian product operation. A?non-empty subset? of a?complete lattice? is called a?complete sublattice of? if and for any non-empty . We prove that? is isomorphic to a?complete sublattice of . On the other hand, it is obvious that is isomorphic to a?complete sublattice of? for any locally finite variety?. We deduce criteria for the existence of an isomorphism onto a?(complete) sublattice of for some locally finite variety?. We also prove that there is a?sublattice generated by four elements and containing an infinite chain.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::10b5a9daae3b208596585be301a97110 https://doi.org/10.1070/im1999v063n04abeh000250 Zobrazit plný text záznamu