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Structural isomorphism

From Encyclopedia of Mathematics
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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]).

References

[1] A.G. Kurosh, "The theory of groups" , 1–2 , Chelsea (1955–1956) (Translated from Russian)


Comments

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.

How to Cite This Entry:
Structural isomorphism. O.A. Ivanova (originator), Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Structural_isomorphism&oldid=16804
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098