#6513 ⟨a, b | aba=b, abbbb=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 ab is not injective:
-
ab ⋅ a2 = ab and ab ⋅ 1 = ab, however a2 ≠ 1
- Gröbner basis: ⟨a, b | a2b=b, b4=ab⟩
- Cancellative quotient is isomorphic to ℤ6
- Enveloping group is isomorphic to ℤ6
- 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:aba=b,abbbb=b ab - -
ba=ab
aab=b
bbbb=ab
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
3 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 6521 | ⟨a, b | aba=b, babbb=b⟩ | φ(a) = a, φ(b) = b |
| 10 | 6523 | ⟨a, b | aba=b, bbabb=b⟩ | φ(a) = a, φ(b) = b |
| 10 | 6796 | ⟨a, b | aba=b, bbbb=ab⟩ | φ(a) = a, φ(b) = b |