Abstract. We show that in a finite semimodular lattice, the ordering of join-irreducible congruences is done in a special type of sublattice, we call a tight $S_7$.

AMS Subject Classification (1991): 06C10, 06B10

Keyword(s): Semimodular lattice, planar, congruence, prime interval

Received April 21, 2007, and in final form January 31, 2008. (Registered under 6001/2009.)