Grigorchuk Group

In group theory, the Grigorchuk group, also called the first Grigorchuk group, is a finitely generated group constructed by Rostislav Grigorchuk that gave the first example of a finitely generated group of intermediate growth, meaning its growth is faster than polynomial but slower than exponential. Grigorchuk constructed the group in 1980 and proved in 1984 that it has intermediate growth, resolving a question John Milnor had posed in 1968 about whether such groups exist. It remains an important example in geometric group theory, particularly in the study of branch groups and automata groups.