#12982 ⟨a, b | abb=aaa, baab=a⟩
Contents
- Properties
- Commutative structure
- Staircase diagram
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 11
- Infinite non-cancellative commutative monoid
- Element b has infinite order
- Not cancellative, because multiplication by a is not injective:
-
a ⋅ a3 = a and a ⋅ 1 = a, however a3 ≠ 1
- Gröbner basis: ⟨a, b | ab2=a3, a4=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 a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:abb=aaa,baab=a ab - -
ba=ab
abb=aaa
aaaa=a
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
5 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 13080 | ⟨a, b | bab=aaa, aaaa=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 13086 | ⟨a, b | bab=aaa, aabb=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 13088 | ⟨a, b | bab=aaa, abab=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 13090 | ⟨a, b | bab=aaa, abba=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 13094 | ⟨a, b | bab=aaa, baab=a⟩ | φ(a) = a, φ(b) = b |