#71 ⟨a, b | ababba=1⟩
Properties
- Presentation has sum-of-sides 6
- Infinite non-Abelian group
- Group inverses:
- a-1 = bcd
- b-1 = ac2
- c-1 = cd
- d-1 = c2
Complete rewriting system
- Reduction order:
- Left-to-right recursive path with deg(c) = deg(d) = 0, c < d; deg(b) = deg(a) = 1, b < a
- Auxiliary generator: ab=c
- Auxiliary generator: ba=d
- dc ⇒ cd
- c2d ⇒ 1
- db ⇒ bc
- c2b ⇒ bcd
- ca ⇒ ad
- da ⇒ ac4
- ba ⇒ d
- ab ⇒ c
# ab:ababba=1 cd/ba ab=c,ba=d frequency:2/0,2/1
dc=cd
ccd=1
db=bc
ccb=bcd
ca=ad
da=acccc
ba=d
ab=c
Right Cayley graph (truncated)
Left Cayley graph (truncated)
Other isomorphic instances
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
1 total
| Σ | # | Presentation | Mapping |
|---|
| 6 | 72 | ⟨a, b | abbaab=1⟩ | φ(a) = a, φ(b) = b |