- LandOfFree
- Scientists
- Mathematics
- Group Theory
Details
Nielsen equivalence in small cancellation groups
Nielsen equivalence in small cancellation groups
2010-11-26
-
arxiv.org/abs/1011.5862v2
Mathematics
Group Theory
28 pages, 15 figures; corrected one reference and added a reference
to Louder
Scientific paper
Let $G$ be a group given by the presentation \[,\] where $k\ge 2$ and where the $u_i\in F(b_1,..., b_k)$ and $w_i\in F(a_1,..., a_k)$ are random words. Generically such a group is a small cancellation group and it is clear that $(a_1,...,a_k)$ and $(b_1,...,b_k)$ are generating $n$-tuples for $G$. We prove that for generic choices of $u_1,..., u_k$ and $v_1,..., v_k$ the "once-stabilized" tuples $(a_1,..., a_k,1)$ and $(b_1,...,b_k,1)$ are not Nielsen equivalent in $G$. This provides a counter-example for a Wiegold-type conjecture in the setting of word-hyperbolic groups. We conjecture that in the above construction at least $k$ stabilizations are needed to make the tuples $(a_1,..., a_k)$ and $(b_1,...,b_k)$ Nielsen equivalent.
Affiliated with
Also associated with
No associations
LandOfFree
Say what you really think
Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.
Rating
Nielsen equivalence in small cancellation groups does not yet have a rating.
At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Nielsen equivalence in small cancellation groups, we encourage you to share that experience with our LandOfFree.com community.
Your opinion is very important and Nielsen equivalence in small cancellation groups will most certainly appreciate the feedback.
Rate now
Profile ID: LFWR-SCP-O-463575
All data on this website is collected from public sources.
Our data reflects the most accurate information available at the time of publication.