Difference between revisions of "Jordan-Dedekind lattice"
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Revision as of 18:52, 24 March 2012
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.
A general reference is [a1]. See also Partially ordered set; Chain.
References
| [a1] | M. Hall, Jr., "The theory of groups" , Macmillan (1968) |
How to Cite This Entry:
Jordan-Dedekind lattice. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Jordan-Dedekind_lattice&oldid=22613
Jordan-Dedekind lattice. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Jordan-Dedekind_lattice&oldid=22613
This article was adapted from an original article by L.M. Batten (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article