#20584 ⟨a, b | ab=aa, baaaaa=a⟩
Contents
- Properties
- Commutative structure
- Staircase diagram
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 11
- Infinite non-cancellative commutative monoid
- Element b has infinite order
- Not cancellative, because multiplication by a is not injective:
-
a ⋅ b = a2 and a ⋅ a = a2, however b ≠ a
- Gröbner basis: ⟨a, b | ab=a2, a6=a⟩
- Cancellative quotient is isomorphic to ℤ5
- Enveloping group is isomorphic to ℤ5
- 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:ab=aa,baaaaa=a ab - -
ab=aa
ba=aa
aaaaaa=a
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
15 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 20586 | ⟨a, b | ab=aa, baaaab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 20588 | ⟨a, b | ab=aa, baaaba=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 20590 | ⟨a, b | ab=aa, baaabb=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 20592 | ⟨a, b | ab=aa, baabaa=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 20594 | ⟨a, b | ab=aa, baabab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 20596 | ⟨a, b | ab=aa, baabba=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 20598 | ⟨a, b | ab=aa, baabbb=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 20600 | ⟨a, b | ab=aa, babaaa=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 20602 | ⟨a, b | ab=aa, babaab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 20604 | ⟨a, b | ab=aa, bababa=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 20606 | ⟨a, b | ab=aa, bababb=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 20608 | ⟨a, b | ab=aa, babbaa=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 20610 | ⟨a, b | ab=aa, babbab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 20612 | ⟨a, b | ab=aa, babbba=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 20614 | ⟨a, b | ab=aa, babbbb=a⟩ | φ(a) = a, φ(b) = b |