#19211 ⟨a, b | aba=b, abbbbb=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 ab is not injective:
-
ab ⋅ a2 = ab and ab ⋅ 1 = ab, however a2 ≠ 1
- Gröbner basis: ⟨a, b | a2b=b, b5=ab⟩
- Cancellative quotient is isomorphic to ℤ8
- Enveloping group is isomorphic to ℤ8
- 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,abbbbb=b ab - -
ba=ab
aab=b
bbbbb=ab
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
3 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 19225 | ⟨a, b | aba=b, babbbb=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 19229 | ⟨a, b | aba=b, bbabbb=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 19774 | ⟨a, b | aba=b, bbbbb=ab⟩ | φ(a) = a, φ(b) = b |