 It is obvious that the growth rate of a finitely generated group is at most exponential and it was also understood early on that finitely generated nilpotent groups have polynomial growth.In 1968 John Milnor posed a question about the existence of a finitely generated group of "intermediate growth", that is, faster than any polynomial function and slower than any exponential function.An important result in the subject is Gromov's theorem on groups of polynomial growth, obtained by Gromov in 1981, which shows that a finitely generated group has polynomial growth if and only if this group has a nilpotent subgroup of finite index.