#20862 ⟨a, b | ba=ab, aaabb=bb⟩
Contents
- Properties
- Commutative structure
- Staircase diagram
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 11
- Infinite non-cancellative commutative monoid
- Element a has infinite order
- Not cancellative, because multiplication by a2b2 is not injective:
-
a2b2 ⋅ a3 = a2b2 and a2b2 ⋅ 1 = a2b2, however a3 ≠ 1
- Gröbner basis: ⟨a, b | a3b2=b2⟩
- Cancellative quotient is isomorphic to ℤ3 ⊕ ℕ
- Enveloping group is isomorphic to ℤ3 ⊕ ℤ
- Group of units is isomorphic to ℤ1
- 3 Archimedian components:
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:ba=ab,aaabb=bb ab - -
ba=ab
aaabb=bb
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
5 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 20869 | ⟨a, b | ba=ab, aabab=bb⟩ | φ(a) = a, φ(b) = b |
| 11 | 20873 | ⟨a, b | ba=ab, aabba=bb⟩ | φ(a) = a, φ(b) = b |
| 11 | 20877 | ⟨a, b | ba=ab, abaab=bb⟩ | φ(a) = a, φ(b) = b |
| 11 | 20880 | ⟨a, b | ba=ab, ababa=bb⟩ | φ(a) = a, φ(b) = b |
| 11 | 20881 | ⟨a, b | ba=ab, abbba=aa⟩ | φ(a) = b, φ(b) = a |