#1519 ⟨a, b | ababbaabba=1⟩
Properties
- Presentation has sum-of-sides 10
- Infinite non-Abelian group
- Group inverses:
- a-1 = bc2d2
- b-1 = ac3d
- c-1 = c2d2
- d-1 = c3d
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
- c3d2 ⇒ 1
- db ⇒ bc
- c3b ⇒ bcd2
- ca ⇒ ad
- cda ⇒ dad
- d2a ⇒ ac6d
- ba ⇒ d
- ab ⇒ c
# ab:ababbaabba=1 cd/ba ab=c,ba=d frequency:2/0,2/1
dc=cd
cccdd=1
db=bc
cccb=bcdd
ca=ad
cda=dad
dda=accccccd
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 |
|---|
| 10 | 1533 | ⟨a, b | abbaabbaab=1⟩ | φ(a) = a, φ(b) = b |