#7020 ⟨a, b | ba=ab, aaabb=a⟩
Contents
- Properties
- Commutative structure
- Staircase diagram
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 10
- Infinite non-cancellative commutative monoid
- Element a has infinite order
- Not cancellative, because multiplication by a is not injective:
-
a ⋅ a2b2 = a and a ⋅ 1 = a, however a2b2 ≠ 1
- Gröbner basis: ⟨a, b | a3b2=a⟩
- Cancellative quotient is isomorphic to ℤ2 ⊕ ℤ
- Enveloping group is isomorphic to ℤ2 ⊕ 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=a ab - -
ba=ab
aaabb=a
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
5 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 7024 | ⟨a, b | ba=ab, aabab=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 7026 | ⟨a, b | ba=ab, aabba=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 7028 | ⟨a, b | ba=ab, abaab=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 7030 | ⟨a, b | ba=ab, ababa=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 7033 | ⟨a, b | ba=ab, abbba=b⟩ | φ(a) = b, φ(b) = a |