#2849 ⟨a, b, c | aaa=b, cac=b⟩
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 | aaaabb⟩
-
Embedding: φ(a) = a-1, φ(b) = a-1a-1a-1, φ(c) = ab
- Reduction order:
- Left-to-right recursive path with deg(a) = deg(c) = 0, a < c; deg(b) = 1
- Certificate: derivations of all rewriting rules from the defining relations.
# abc:aaa=b,cac=b ac/b - -
cac=aaa
caaaa=aaaac
b=aaa
10 unique, 115 total
| Σ | # | Presentation | Properties | φ |
|---|
| 7 | 366 | ⟨a, b, c | aba=b, cbc=1⟩ | Grp Inf | 93 |
| 7 | 548 | ⟨a, b, c | bb=aa, cc=a⟩ | Can Inf | 1 |
| 7 | 938 | ⟨a, b, c | aa=b, cbc=b⟩ | Can Inf | 5 |
| 8 | 2851 | ⟨a, b, c | aaa=b, cbc=a⟩ | Can Inf | 3 |
| 8 | 3041 | ⟨a, b, c | aba=b, cac=b⟩ | Can Inf | |
| 8 | 3042 | ⟨a, b, c | aba=b, cbc=a⟩ | Can Inf | 1 |
| 8 | 3472 | ⟨a, b, c | ba=ac, cab=a⟩ | Can Inf | |
| 8 | 3501 | ⟨a, b, c | bb=ac, aaa=c⟩ | Can Inf | 2 |
| 8 | 3594 | ⟨a, b, c | ba=ac, cb=aa⟩ | Can Inf | |
| 8 | 6095 | ⟨a, b, c | ab=c, bcc=ca⟩ | Can Inf | |
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
2 total
| Σ | # | Presentation | Mapping |
|---|
| 8 | 5759 | ⟨a, b, c | aa=b, cac=ab⟩ | φ(a) = a, φ(b) = aa, φ(c) = c |
| 8 | 5992 | ⟨a, b, c | ab=c, aaa=bc⟩ | φ(a) = a, φ(b) = c, φ(c) = ac |