#4667 ⟨a, b | aaab=a, babb=a⟩
Contents
- Properties
- Commutative structure
- Staircase diagram
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 10
- Infinite non-cancellative commutative monoid
- Element b has infinite order
- Not cancellative, because multiplication by ab is not injective:
-
ab ⋅ a2 = a and ab ⋅ b2 = a, however a2 ≠ b2
- Gröbner basis: ⟨a, b | a3=ab2, ab3=a⟩
- 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 b < a
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:aaab=a,babb=a ba - -
ab=ba
aaa=bba
bbba=a
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
3 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 13082 | ⟨a, b | bab=aaa, aaab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 13084 | ⟨a, b | bab=aaa, aaba=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 13096 | ⟨a, b | bab=aaa, babb=a⟩ | φ(a) = a, φ(b) = b |