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Andrews-Curtis Groups
Robert H. Gilman, Alexei G. Myasnikov
https://arxiv.org/abs/2506.23031 https://arxiv.org/pdf/2506.23031

Andrews-Curtis Groups
For any group $G$ and integer $k\ge 2$ the Andrews-Curtis transformations act as a permutation group, termed the Andrews-Curtis group $AC_k(G)$, on the subset $N_k(G) \subset G^k$ of all $k$-tuples that generate $G$ as a normal subgroup (provided $N_k(G)$ is non-empty). The famous Andrews-Curtis Conjecture is that if $G$ is free of rank $k$, then $AC_k(G)$ acts transitively on $N_k(G)$. The set $N_k(G)$ may have a rather complex structure, so it is easier to study the full Andrews-Curtis group …

Replaced article(s) found for math.GR. https://arxiv.org/list/math.GR/new
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- Andrews-Curtis groups
Robert H. Gilman, Alexei G. Myasnikov