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The lattice of convex sublattices of a lattice. (Russian) Zbl 0711.06005
For a lattice L let Sub L and CSub L be the lattice of all sublattices of L or the lattice of all convex sublattices of L, respectively (including the empty set). The author is interested in the question to what extent the lattice L is determined by CSub L. Typical results: Let L and $$L'$$ be lattices; then CSub $$L\simeq CSub L'$$ iff there exists a bijection f: $$L\to L'$$ such that $$f([a\wedge b,a\vee b])=[f(a)\wedge f(b),f(a)\vee f(b)]$$ for each a,b$$\in L$$. Let L be a discrete modular lattice; then L is determined up to isomorphism by CSub L iff some of the following conditions is valid: (i) each direct factor of L is selfdual; (ii) each directly indecomposable direct factor of L is selfdual. Next, the author investigates the relations between the groups of automorphisms of the lattices L, Conv L and CSub L.
Reviewer: J.Jakubík

##### MSC:
 06B05 Structure theory of lattices 06C05 Modular lattices, Desarguesian lattices
##### Keywords:
automorphism groups; convex sublattices; modular lattice