Structural isomorphism

An obsolete name for a lattice isomorphism, cf. Subalgebra lattice.

With regard to groups, the question of when isomorphism of two groups follows from their lattice isomorphism, i.e. the fact that their lattices of subgroups are isomorphic, has been studied (see [1]).

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The phrase "structural isomorphism" comes from the obsolete term structure for lattice, cf. [1], Vol. 2, p. 85. Some results on when lattice-isomorphic groups are isomorphic are listed in [1], Vol. 2, pp. 88-89.