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Nielsen equivalence in small cancellation groups

# Nielsen equivalence in small cancellation groups,Ilya Kapovich,Richard Weidmann

Nielsen equivalence in small cancellation groups
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.
Published in 2010.
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## References (13)

### Freely Indecomposable Groups Acting on Hyperbolic Spaces(Citations: 12)

Journal: International Journal of Algebra and Computation - IJAC , vol. 14, no. 2, pp. 115-171, 2004

### Variants of Product Replacement(Citations: 7)

Published in 2002.

### Nielsen equivalence in fuchsian groups and seifert fibered spaces(Citations: 16)

Journal: Topology , vol. 30, no. 2, pp. 191-204, 1991

### What Do We Know about the Product Replacement Algorithm(Citations: 4)

Published in 1999.

### Subgroups of small Cancellation Groups(Citations: 94)

Journal: Bulletin of The London Mathematical Society - BULL LOND MATH SOC , vol. 14, no. 1, pp. 45-47, 1982