#20662 ⟨a, b | ba=ab, aaabbb=a⟩
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 a is not injective:
-
a ⋅ a2b3 = a and a ⋅ 1 = a, however a2b3 ≠ 1
- Gröbner basis: ⟨a, b | a3b3=a⟩
- Cancellative quotient is isomorphic to ℤ
- Enveloping group is isomorphic to 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,aaabbb=a ab - -
ba=ab
aaabbb=a
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
9 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 20667 | ⟨a, b | ba=ab, aababb=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 20670 | ⟨a, b | ba=ab, aabbab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 20671 | ⟨a, b | ba=ab, aabbab=b⟩ | φ(a) = b, φ(b) = a |
| 11 | 20672 | ⟨a, b | ba=ab, aabbba=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 20673 | ⟨a, b | ba=ab, aabbba=b⟩ | φ(a) = b, φ(b) = a |
| 11 | 20678 | ⟨a, b | ba=ab, ababab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 20679 | ⟨a, b | ba=ab, ababba=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 20680 | ⟨a, b | ba=ab, ababba=b⟩ | φ(a) = b, φ(b) = a |
| 11 | 20681 | ⟨a, b | ba=ab, abbaab=a⟩ | φ(a) = a, φ(b) = b |