#6917 ⟨a, b | ba=ab, aaabbb=1⟩
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- Properties
- Staircase diagram
- Rewriting system
- Isomorphic instances
- Presentation has sum-of-sides 10
- Isomorphic to ℤ3 ⊕ ℤ
- Infinite Abelian group
- Inverses of generators:
- Commutative Gröbner basis: ⟨a, b | a3b3=1⟩
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:ba=ab,aaabbb=1 ab
ba=ab
aaabbb=1
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
6 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 6920 | ⟨a, b | ba=ab, aababb=1⟩ | φ(a) = a, φ(b) = b |
| 10 | 6922 | ⟨a, b | ba=ab, aabbab=1⟩ | φ(a) = a, φ(b) = b |
| 10 | 6923 | ⟨a, b | ba=ab, aabbba=1⟩ | φ(a) = a, φ(b) = b |
| 10 | 6926 | ⟨a, b | ba=ab, ababab=1⟩ | φ(a) = a, φ(b) = b |
| 10 | 6927 | ⟨a, b | ba=ab, ababba=1⟩ | φ(a) = a, φ(b) = b |
| 10 | 6928 | ⟨a, b | ba=ab, abbaab=1⟩ | φ(a) = a, φ(b) = b |