#3071 ⟨a, b, c | abc=b, bca=c⟩
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 | aaabb⟩
-
Embedding: φ(a) = aba, φ(b) = ab, φ(c) = b-1a-1a-1
- Auxiliary generators:
- d = bc
- Reduction order:
- Left-to-right recursive path with deg(a) = deg(d) = 0, a < d; deg(c) = deg(b) = 1, c < b
- Certificate: derivations of all rewriting rules from the defining relations.
- Morphocompletion: how the auxiliary generators were found.
# abc:abc=b,bca=c ad/cb bc=d morph:2/0
adda=d
ddda=addd
c=da
b=ad
12 unique, 171 total
| Σ | # | Presentation | Properties | φ |
|---|
| 7 | 279 | ⟨a, b, c | aaa=b, cbc=1⟩ | Grp Inf | 146 |
| 7 | 543 | ⟨a, b, c | ba=ac, cb=a⟩ | Can Inf | |
| 7 | 555 | ⟨a, b, c | bb=ac, cb=a⟩ | Can Inf | 4 |
| 7 | 558 | ⟨a, b, c | bb=ac, cc=a⟩ | Can Inf | 2 |
| 7 | 937 | ⟨a, b, c | aa=b, cbc=a⟩ | Can Inf | 2 |
| 7 | 1042 | ⟨a, b, c | ab=c, bcc=a⟩ | Can Inf | 2 |
| 8 | 3045 | ⟨a, b, c | aba=c, abc=b⟩ | Can Inf | 2 |
| 8 | 3051 | ⟨a, b, c | aba=c, bab=c⟩ | Can Inf | |
| 8 | 3595 | ⟨a, b, c | ba=ac, cb=ac⟩ | Can Inf | |
| 8 | 5663 | ⟨a, b, c | aa=b, aaa=cc⟩ | Can Inf | 1 |
| 8 | 6019 | ⟨a, b, c | ab=c, aba=bc⟩ | Can Inf | |
| 8 | 6071 | ⟨a, b, c | ab=c, bac=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 | 5210 | ⟨a, b, c | aa=b, acca=c⟩ | φ(a) = a, φ(b) = aa, φ(c) = d |
| 8 | 5520 | ⟨a, b, c | ab=c, abba=b⟩ | φ(a) = a, φ(b) = d, φ(c) = ad |