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Results tagged with free-groups
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user 7644
11
votes
0
answers
376
views
Ascending chain condition for 1-element normal closures in a free group
Let $F$ be a free group of finite rank. Does $F$ satisfy the ascending chain condition on normal subgroups each of which is a normal closure of one element?
In other words, can there exist elements $ …
- 3,181
7
votes
Accepted
Products of subgroups of a free group
The answer is negative even if $A$ is finitely generated. Here is a simple construction.
Let $F$ be the free group on $\{x,y,z\}$ and let $A=\langle x,y \rangle$. Then there is a natural retraction $ …
- 3,181
7
votes
3
answers
514
views
Membership to double cosets in free groups
Is there an elementary and efficient algorithm for testing the membership to a double coset of f.g. subgroups in a free group?
Has this membership problem been implemented in GAP/Magma?
More precise …
- 3,181
4
votes
Accepted
Measuring products of finitely generated subgroups of free groups
The answer is yes.
Let's prove this by induction on $n$. If $n=1$, then by M. Hall's theorem there is a finite index subgroup $K \leqslant F$ such that $H_1 \subseteq K$ and $|F:K|>1/\epsilon$. Choo …
- 3,181