Name
Abstract | ||
|---|---|---|
Let $G$ be the first Grigorchuk group. We show that the commutator width of $G$ is $2$: every element $gin [G,G]$ is a product of two commutators, and also of six conjugates of $a$. Furthermore, we show that every finitely generated subgroup $Hleq G$ has finite commutator width, which however can be arbitrarily large, and that $G$ contains a subgroup of infinite commutator width. The proofs were assisted by the computer algebra system GAP. |
Year | Venue | Field |
|---|---|---|
2017 | arXiv: Group Theory | Grigorchuk group,Finitely-generated abelian group,Algebra,Symbolic computation,Pure mathematics,Mathematical proof,Commutator (electric),Mathematics,Arbitrarily large |
DocType | Volume | Citations |
Journal | abs/1710.05706 | 0 |
PageRank | References | Authors |
0.34 | 0 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Laurent Bartholdi | 1 | 27 | 8.74 |
| Thorsten Groth | 2 | 0 | 0.34 |
| Igor Lysenok | 3 | 0 | 0.34 |