#3587 ⟨a, b, c | ba=ab, cc=ab⟩
Contents
- Properties
- Rewriting system
- Other submonoids of same group
- Isomorphic instances
- Sum of relation sides is 8
- Infinite cancellative non-commutative monoid
- Element a has infinite order
- Submonoid of enveloping group: ⟨a, b | aaba-1a-1b-1⟩
-
Embedding: φ(a) = a-1a-1b-1, φ(b) = b, φ(c) = a-1
- Reduction order:
- Left-to-right shortlex with c < a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# abc:ba=ab,cc=ab cab - -
ab=cc
ba=cc
acc=cca
bcc=ccb
8 unique, 15 total
| Σ | # | Presentation | Properties | φ |
|---|
| 7 | 533 | ⟨a, b, c | ba=ab, cc=a⟩ | Can Inf | |
| 8 | 2199 | ⟨a, b, c | aabc=1, acba=1⟩ | Grp Inf | 5 |
| 8 | 2976 | ⟨a, b, c | aab=c, baa=c⟩ | Can Inf | 2 |
| 8 | 3072 | ⟨a, b, c | abc=b, cba=b⟩ | Can Inf | |
| 8 | 3431 | ⟨a, b, c | ba=ab, cac=b⟩ | Can Inf | |
| 8 | 3592 | ⟨a, b, c | ba=ac, ca=ab⟩ | Can Inf | |
| 8 | 3596 | ⟨a, b, c | ba=ac, cc=bb⟩ | Can Inf | |
| 8 | 6088 | ⟨a, b, c | ab=c, bca=cc⟩ | Can Inf | |
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
1 total
| Σ | # | Presentation | Mapping |
|---|
| 8 | 3601 | ⟨a, b, c | bb=ac, ca=bb⟩ | φ(a) = a, φ(b) = c, φ(c) = b |