#1519 ⟨a, b | ababbaabba=1⟩
Quick links
- Properties
- Rewriting system
- Isomorphic instances
- Presentation has sum-of-sides 10
- Infinite non-Abelian group
- Inverses of generators:
- a-1 = c2bc2
- b-1 = acd
- c-1 = cd
- d-1 = c2
- Reduced group presentation: ⟨a, b | aabab-1abab-1⟩
- Isomorphism: φ(a) = b-1a, φ(b) = b
- Auxiliary generators:
- c = ba
- d = bcca
- Reduction order:
- Left-to-right recursive path with deg(c) = deg(d) = 0, c < d; deg(a) = 1; deg(b) = 2
- Certificate: derivations of all rewriting rules from the defining relations.
- Morphocompletion: how the auxiliary generators were found.
# ab:ababbaabba=1 cd/a/b ba=c,bcca=d morph:2/0,4/0
dc=cd
ccd=1
da=accc
cca=acdd
ba=c
cbca=bcac
db=cbcc
cccb=bd
abca=cac
accb=d
cab=abc
cacb=acbc
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
2 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 1532 | ⟨a, b | abbaababba=1⟩ | φ(a) = acdba, φ(b) = b |
| 10 | 1533 | ⟨a, b | abbaabbaab=1⟩ | φ(a) = acdba, φ(b) = b |