UL-equivalent group

Symbol-free definition
A group is said to be UL-equivalentif it is nilpotent and its upper central series and lower central series actually coincide. In other words, if the nilpotence class is $$c$$, the $$k^{th}$$ term of the fact about::upper central series equals the $$(c+1-k)^{th}$$ term of the fact about::lower central series. (Note that we start counting the lower central series from $$1$$ at the group, and the upper central series at $$0$$ from the trivial subgroup).