#662 ⟨a, b | aabaabbaa=1⟩
Properties
- Presentation has sum-of-sides 9
- Infinite non-Abelian group
- Group inverses:
- a-1 = ac2b
- b-1 = dca2
- c-1 = dc
- d-1 = c2
Complete rewriting system
- Reduction order:
- Right-to-left recursive path with deg(a) = deg(c) = deg(d) = 0, a < c < d; deg(b) = 1
- Auxiliary generator: aab=c
- Auxiliary generator: baa=d
- cd ⇒ dc
- dc2 ⇒ 1
- a2d ⇒ ca2
- a2c2 ⇒ dca2
- a2b ⇒ c
- ba ⇒ dac2b
- bc ⇒ db
- bd ⇒ c4b
# ab:aabaabbaa=1 reversed:acd/b aab=c,baa=d frequency:3/0,3/3
cd=dc
dcc=1
aad=caa
aacc=dcaa
aab=c
ba=daccb
bc=db
bd=ccccb
Right Cayley graph (truncated)
Left Cayley graph (truncated)
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 |
|---|
| 9 | 698 | ⟨a, b | abaaaabba=1⟩ | φ(a) = a, φ(b) = b |