I(L)-topological groups and its level L-topological groups

In this paper, we discuss the relationship between an I(L)-topological group and its level L-topological groups. We supply a method to generate an I(L)-topological group by a co-tower of group L-topologies and obtain a necessary and sufficient condition for the I(L)-topological group generated by a co-tower of group L-topologies to be L-topologically generated.