#1346 ⟨a, b | aaabaababa=1⟩
Properties
- Presentation has sum-of-sides 10
- Infinite non-Abelian group
- Group inverses:
- a-1 = a2d
- b-1 = a4cac
- c-1 = a3cac
- d-1 = a3
Complete rewriting system
- Reduction order:
- Right-to-left recursive path with deg(d) = deg(a) = 0, d < a; deg(c) = 1; deg(b) = 2
- Auxiliary generator: ba=c
- Auxiliary generator: cacc=d
- da ⇒ ad
- a3d ⇒ 1
- cacd ⇒ adc2
- ca3ca ⇒ a3cac
- (ca)2d ⇒ adc2a
- c2a2 ⇒ a2dca3c
- caca2d ⇒ dca3c
- cac2 ⇒ d
- c(aca)2 ⇒ dca6cac
- b ⇒ ca2d
# ab:aaabaababa=1 reversed:da/c/b ba=c,cacc=d frequency:2/0,4/0
da=ad
aaad=1
cacd=adcc
caaaca=aaacac
cacad=adcca
ccaa=aadcaaac
cacaad=dcaaac
cacc=d
cacaaca=dcaaaaaacac
b=caad
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.
2 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 1406 | ⟨a, b | aabaababaa=1⟩ | φ(a) = a, φ(b) = caad |
| 10 | 1479 | ⟨a, b | abaaaabaab=1⟩ | φ(a) = a, φ(b) = aadc |
Other anti-isomorphic instances
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
1 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 1480 | ⟨a, b | abaaaababa=1⟩ | φ(a) = a, φ(b) = cdaa |