Nilpotent groups are a special class of groups in which the lower central series eventually becomes trivial. More specifically, a group is nilpotent if its derived series reaches the identity after finitely many steps. This property connects to the concepts of amenability and ergodic theory, particularly through the understanding of group actions and the behavior of Følner sequences within amenable groups, as well as the mean ergodic theorem that applies to them.
congrats on reading the definition of nilpotent groups. now let's actually learn it.