#5060 ⟨a, b | aaa=ab, baab=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 a is not injective:
-
a ⋅ a5 = a and a ⋅ 1 = a, however a5 ≠ 1
- Gröbner basis: ⟨a, b | a6=a, ab=a3⟩
- Cancellative quotient is isomorphic to ℤ5
- Enveloping group is isomorphic to ℤ5
- 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:aaa=ab,baab=a a/b - -
aaaaaa=a
ba=aaa
ab=aaa
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
9 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 5062 | ⟨a, b | aaa=ab, baba=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 12307 | ⟨a, b | aaab=bb, abba=b⟩ | φ(a) = b, φ(b) = a |
| 11 | 12409 | ⟨a, b | aaba=bb, abab=b⟩ | φ(a) = b, φ(b) = a |
| 11 | 12411 | ⟨a, b | aaba=bb, abba=b⟩ | φ(a) = b, φ(b) = a |
| 11 | 14761 | ⟨a, b | abab=a, baaaa=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 14860 | ⟨a, b | abba=b, abbbb=b⟩ | φ(a) = b, φ(b) = a |
| 11 | 14868 | ⟨a, b | abba=b, babbb=b⟩ | φ(a) = b, φ(b) = a |
| 11 | 14870 | ⟨a, b | abba=b, bbabb=b⟩ | φ(a) = b, φ(b) = a |
| 11 | 15473 | ⟨a, b | aaa=ab, baaaa=a⟩ | φ(a) = a, φ(b) = b |