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.
Facts
Origin Yearoriginally constructed by Grigorchuk in a 1980 paper Classification
Object KindStructure or Algebraic Object 1 Connections
Attributed To
Source Grigorchuk Group (Wikipedia)
In Branch
Source Grigorchuk Group (Wikipedia)
Is Kind Of Object
Sources
1. Grigorchuk Group (Wikipedia)
Lead section
In the mathematical area of group theory, the Grigorchuk group or the first Grigorchuk group is a finitely generated group constructed by Rostislav Grigorchuk that provided the first example of a finitely generated group of intermediate (that is, faster than polynomial but slower than exponential) growth.
In Branch: Group Theory, Lead sentence
In the mathematical area of group theory, the Grigorchuk group or the first Grigorchuk group is a finitely generated group constru
Attributed To: Rostislav Grigorchuk, Lead sentence, attribution
constructed by Rostislav Grigorchuk
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