#95 ⟨a, b | aa=1, bbb=b⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 6
- Isomorphic to ℤ2 ∗ ℕ(3 = 1)
- Infinite non-cancellative non-commutative monoid
- Element ba has infinite order
- Not left cancellative, because left multiplication by b is not injective:
-
b ⋅ b2 = b and b ⋅ 1 = b, however b2 ≠ 1
- Not right cancellative, because right multiplication by b is not injective:
-
b2 ⋅ b = b and 1 ⋅ b = b, however b2 ≠ 1
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:aa=1,bbb=b ab - -
aa=1
bbb=b
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
23 total
| Σ | # | Presentation | Mapping |
|---|
| 8 | 1111 | ⟨a, b | aa=1, aabbb=b⟩ | φ(a) = a, φ(b) = b |
| 8 | 1127 | ⟨a, b | aa=1, baabb=b⟩ | φ(a) = a, φ(b) = b |
| 8 | 1191 | ⟨a, b | aa=1, abbb=ab⟩ | φ(a) = a, φ(b) = b |
| 8 | 1254 | ⟨a, b | aa=1, bbb=aab⟩ | φ(a) = a, φ(b) = b |
| 10 | 9671 | ⟨a, b | aa=1, aaaabbb=b⟩ | φ(a) = a, φ(b) = b |
| 10 | 9693 | ⟨a, b | aa=1, aabaabb=b⟩ | φ(a) = a, φ(b) = b |
| 10 | 9703 | ⟨a, b | aa=1, aabbaab=b⟩ | φ(a) = a, φ(b) = b |
| 10 | 9709 | ⟨a, b | aa=1, aabbbaa=b⟩ | φ(a) = a, φ(b) = b |
| 10 | 9763 | ⟨a, b | aa=1, baaaabb=b⟩ | φ(a) = a, φ(b) = b |
| 10 | 9769 | ⟨a, b | aa=1, baabaab=b⟩ | φ(a) = a, φ(b) = b |
| 10 | 9956 | ⟨a, b | aa=1, aaabbb=ab⟩ | φ(a) = a, φ(b) = b |
| 10 | 9980 | ⟨a, b | aa=1, aabbba=ba⟩ | φ(a) = a, φ(b) = b |
| 10 | 9994 | ⟨a, b | aa=1, abaabb=ab⟩ | φ(a) = a, φ(b) = b |
| 10 | 10010 | ⟨a, b | aa=1, abbaab=ab⟩ | φ(a) = a, φ(b) = b |
| 10 | 10213 | ⟨a, b | aa=1, aaaab=bbb⟩ | φ(a) = a, φ(b) = b |
| 10 | 10235 | ⟨a, b | aa=1, aabaa=bbb⟩ | φ(a) = a, φ(b) = b |
| 10 | 10253 | ⟨a, b | aa=1, aabbb=aab⟩ | φ(a) = a, φ(b) = b |
| 10 | 10256 | ⟨a, b | aa=1, aabbb=baa⟩ | φ(a) = a, φ(b) = b |
| 10 | 10292 | ⟨a, b | aa=1, abbba=aba⟩ | φ(a) = a, φ(b) = b |
| 10 | 10311 | ⟨a, b | aa=1, baabb=aab⟩ | φ(a) = a, φ(b) = b |
| 10 | 10314 | ⟨a, b | aa=1, baabb=baa⟩ | φ(a) = a, φ(b) = b |
| 10 | 10492 | ⟨a, b | aa=1, abbb=aaab⟩ | φ(a) = a, φ(b) = b |
| 10 | 10495 | ⟨a, b | aa=1, abbb=abaa⟩ | φ(a) = a, φ(b) = b |