#1305 ⟨a, b, c | ab=1, abca=c⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 7
- Infinite non-cancellative non-commutative monoid
- Element a has infinite order
- Not left cancellative, because left multiplication by c is not injective:
-
c ⋅ a = c and c ⋅ 1 = c, however a ≠ 1
- Not right cancellative, because right multiplication by b is not injective:
-
ba ⋅ b = b and 1 ⋅ b = b, however ba ≠ 1
- Reduction order:
- Left-to-right shortlex with a < b < c
- Certificate: derivations of all rewriting rules from the defining relations.
# abc:ab=1,abca=c abc - -
ab=1
ca=c
cb=c
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
2 total
| Σ | # | Presentation | Mapping |
|---|
| 7 | 1465 | ⟨a, b, c | ab=1, abc=ca⟩ | φ(a) = a, φ(b) = b, φ(c) = c |
| 7 | 1519 | ⟨a, b, c | ab=1, bca=bc⟩ | φ(a) = a, φ(b) = b, φ(c) = c |