#20654 ⟨a, b | ba=ab, aaaabb=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 ⋅ a3b2 = a and a ⋅ 1 = a, however a3b2 ≠ 1
- Gröbner basis: ⟨a, b | a4b2=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,aaaabb=a ab - -
ba=ab
aaaabb=a
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
8 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 20658 | ⟨a, b | ba=ab, aaabab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 20660 | ⟨a, b | ba=ab, aaabba=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 20663 | ⟨a, b | ba=ab, aabaab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 20665 | ⟨a, b | ba=ab, aababa=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 20668 | ⟨a, b | ba=ab, aabbaa=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 20674 | ⟨a, b | ba=ab, abaaab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 20676 | ⟨a, b | ba=ab, abaaba=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 20683 | ⟨a, b | ba=ab, abbbba=b⟩ | φ(a) = b, φ(b) = a |