# Jordan-Dedekind lattice

From Encyclopedia of Mathematics

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A lattice satisfying the following condition, known as the Jordan–Dedekind chain condition: All maximal chains have the same length.

The condition arose in connection with the Jordan–Hölder theorems for groups (cf. Jordan–Hölder theorem), and is equivalent to the condition of supersolvability in the lattice of all subgroups of a finite group (cf Supersolvable group).

A general reference is [a1]. See also Partially ordered set; Chain.

#### References

[a1] | M. Hall, Jr., "The theory of groups" , Macmillan (1964) Zbl 0116.25403 |

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Jordan–Dedekind lattice.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Jordan%E2%80%93Dedekind_lattice&oldid=22614