Abstract. We present some new families of collapsing monoids. These monoids form large intervals in the submonoid lattices of the full transformation semigroups. Some of these intervals have cardinalities $\ge2^{2^{cn}}$ where $n$ is the size of the base set.

AMS Subject Classification (1991): 08A40

Received March 28, 2001, and in revised form July 25, 2001. (Registered under 2856/2009.)