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Results tagged with combinatorial-group-theory
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user 15728
2
votes
2
answers
1k
views
quotient groups of the lower central series of a free group
I have a question about some quotient groups of the lower central series of a free group.
When there's a free group $F = \langle x_1,\cdots, x_n, y_1, \cdots, y_m\rangle $,
let $A$ be the subgroup g …
- 7,217
1
vote
1
answer
293
views
When $[G_k,G_m] = G_{k+m}$?
Hello?
I have a simple question about combinatorial group theory.
For a group $G$, I saw $[G_k, G_m] \subset G_{k+m}$ and these two subgroups need not be equal.
Then is there any known condition that …
- 37.4k
1
vote
1
answer
992
views
Any subgroup of f.g. free group with finite index contains a term of lower central series?
Hello?
I have some questions in the group theory.
I know that the intersection of the lower central series of a finitely generate free group is trivial.
So I wonder whether every nontrivial subgroup o …
- 7,217