A compound of the formula:wherein Ar is an aromatic ring
assembly group which may be substituted or a fused aromatic group which may be substituted; X is (i) a bond, (ii) -S-, -SO- or -SO2-, (iii) C1-6 alkylene, C2-6 alkenylene or C2-6 alkynylene, etc., (iv) -CO-O- or (v) -(CH2)p-X1-, -(CH2)p-X1- (CH2)q-, -(CH2)r-CO-X1-, -SO2-NR8- or -(CH2)r-SO2-NR8- wherein X1 is O or NR8, R8 is H, a
hydrocarbon group which may be substituted or an acyl, p is 0 to 5, q is 1 to 5, p+q is 1 to 5, and r is 1 to 4; Y is a
divalent C1-6
aliphatic hydrocarbon group optionally containing O or S, which may be substituted; R1 and R2 each is H or a lower
alkyl which may be substituted, or R1 and R2 form a N-containing heterocyclic ring which may be substituted; Ring A is a
benzene ring which may be further substituted; and Ring B is a 4- to 8-membered ring which may be further substituted, or a salt thereof has the effect of inhibiting
amyloid-beta
protein production and / or
secretion and is useful as a pharmaceutical composition for preventing and / or treating the neurodegenerative
disease, etc.