#331 ⟨a, b | abababba=1⟩
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- Properties
- Rewriting system
- Other submonoids of same group
- Isomorphic instances
- Presentation has sum-of-sides 8
- Infinite non-Abelian group
- Inverses of generators:
- a-1 = cdb
- b-1 = cdad2
- c-1 = cd
- d-1 = c2
- Reduced group presentation: ⟨a, b | aaabab-1⟩
- Isomorphism: φ(a) = b-1a, φ(b) = b
- Auxiliary generators:
- c = ba
- d = bca
- Reduction order:
- Right-to-left recursive path with deg(d) = deg(c) = 0, d < c; deg(a) = deg(b) = 1, a < b
- Certificate: derivations of all rewriting rules from the defining relations.
- Morphocompletion: how the auxiliary generators were found.
# ab:abababba=1 reversed:dc/ab ba=c,bca=d morph:2/0,3/0
dc=cd
ccd=1
ac=cdad
addd=cca
bd=ccccccb
bc=cddb
ba=c
addb=c
1 unique, 1 total
| Σ | # | Presentation | Description | Related |
|---|
| 6 | 79 | ⟨a, b | aaaba=b⟩ | Infinite cancellative non-commutative monoid | |
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
1 total
| Σ | # | Presentation | Mapping |
|---|
| 8 | 332 | ⟨a, b | ababbaab=1⟩ | φ(a) = cdaddba, φ(b) = b |