#485 ⟨a, b | aabb=1, abba=1⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 8
- Infinite non-Abelian group
- Element a has infinite order
- Inverses of generators:
- a-1 = ca
- b-1 = a2b
- c-1 = a2
- Auxiliary generators:
- c = bb
- Reduction order:
- Left-to-right shortlex with c < a < b
- Certificate: derivations of all rewriting rules from the defining relations.
- Morphocompletion: how the auxiliary generators were found.
# ab:aabb=1,abba=1 cab bb=c morph:2/0
ac=ca
bc=cb
bb=c
caa=1
baa=aab
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
14 total
| Σ | # | Presentation | Mapping |
|---|
| 8 | 487 | ⟨a, b | aabb=1, bbaa=1⟩ | φ(a) = a, φ(b) = b |
| 8 | 490 | ⟨a, b | abba=1, baab=1⟩ | φ(a) = a, φ(b) = b |
| 10 | 4083 | ⟨a, b | baa=aab, aabb=1⟩ | φ(a) = a, φ(b) = b |
| 10 | 4085 | ⟨a, b | baa=aab, abba=1⟩ | φ(a) = a, φ(b) = b |
| 10 | 4087 | ⟨a, b | baa=aab, baab=1⟩ | φ(a) = a, φ(b) = b |
| 10 | 5882 | ⟨a, b | aabb=1, abbaa=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 5888 | ⟨a, b | aabb=1, baaba=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 5892 | ⟨a, b | aabb=1, bbaaa=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 5932 | ⟨a, b | abba=1, aaabb=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 5938 | ⟨a, b | abba=1, aabba=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 5941 | ⟨a, b | abba=1, aabbb=b⟩ | φ(a) = a, φ(b) = b |
| 10 | 5942 | ⟨a, b | abba=1, abaab=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 5949 | ⟨a, b | abba=1, abbab=b⟩ | φ(a) = a, φ(b) = b |
| 10 | 5957 | ⟨a, b | abba=1, baabb=b⟩ | φ(a) = a, φ(b) = b |