Congruence class sizes in finite sectionally complemented lattices

The congruences of a finite sectionally complemented lattice L are not necessarily uniform (any two congruence classes of a congruence are of the same size). To measure how far a congruence Theta of L is from being uniform, we introduce Spec Theta, the spectrum of Theta, the family of cardinalities of the congruence classes of Theta A typical result of this paper characterizes the spectrum S = (m(j) \ j < n) of a nontrivial congruence Θ with the following two properties: (S-1) 2 ≤ n and n ¬equal; 3. (S-2) 2 ≤ mj and mj ¬equal; 3, for all j < n.