#5287 ⟨a, b | aba=bb, abbb=b⟩
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 b is not injective:
-
b ⋅ a5 = b and b ⋅ 1 = b, however a5 ≠ 1
- Gröbner basis: ⟨a, b | b6=b, ab=b4⟩
- 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 recursive path with deg(a) = 0; deg(b) = 1
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:aba=bb,abbb=b a/b - -
baaaaa=b
ab=ba
bb=baa
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
13 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 5291 | ⟨a, b | aba=bb, babb=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 12180 | ⟨a, b | aaaa=ab, baaa=a⟩ | φ(a) = b, φ(b) = a |
| 11 | 14447 | ⟨a, b | aaab=a, baabb=a⟩ | φ(a) = b, φ(b) = a |
| 11 | 14451 | ⟨a, b | aaab=a, babab=a⟩ | φ(a) = b, φ(b) = a |
| 11 | 14453 | ⟨a, b | aaab=a, babba=a⟩ | φ(a) = b, φ(b) = a |
| 11 | 14579 | ⟨a, b | aaba=a, babab=a⟩ | φ(a) = b, φ(b) = a |
| 11 | 15758 | ⟨a, b | aab=bb, ababa=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 15912 | ⟨a, b | aba=bb, aaabb=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 15916 | ⟨a, b | aba=bb, aabab=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 15918 | ⟨a, b | aba=bb, aabba=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 15922 | ⟨a, b | aba=bb, abaab=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 15924 | ⟨a, b | aba=bb, ababa=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 15934 | ⟨a, b | aba=bb, baaab=b⟩ | φ(a) = a, φ(b) = b |