#15932 ⟨a, b | aba=bb, abbbb=b⟩
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 b is not injective:
-
b ⋅ b = ba2 and b ⋅ a2 = ba2, however b ≠ a2
- Gröbner basis: ⟨a, b | b8=b, ab=b5⟩
- Cancellative quotient is isomorphic to ℤ7
- Enveloping group is isomorphic to ℤ7
- 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,abbbb=b a/b - -
baaaaaaa=b
ab=ba
bb=baa
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
2 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 15940 | ⟨a, b | aba=bb, babbb=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 15942 | ⟨a, b | aba=bb, bbabb=b⟩ | φ(a) = a, φ(b) = b |