#639 ⟨a, b | aaababbba=1⟩
Properties
- Presentation has sum-of-sides 9
- Infinite non-Abelian group
- Group inverses:
- a-1 = a3d
- b-1 = cbab2
- c-1 = d
- d-1 = c
Complete rewriting system
- Reduction order:
- Right-to-left recursive path with deg(c) = deg(d) = deg(a) = 0, c < d < a; deg(b) = 1
- Auxiliary generator: aaaa=c
- Auxiliary generator: babbb=d
- dc ⇒ 1
- cd ⇒ 1
- ca ⇒ ac
- da ⇒ ad
- a4 ⇒ c
- bcba ⇒ cbab
- baba3 ⇒ d(bc)2
- b3c ⇒ a3bab2
- bab2d ⇒ adb3
- b3ac ⇒ a3bab2a
- bab2ad ⇒ adb3a
- b3a2c ⇒ a3bab2a2
- bab2a2d ⇒ adb3a2
- b3a3 ⇒ a3db2cb
- bab2a3 ⇒ db(bc)2
- bab3 ⇒ d
# ab:aaababbba=1 reversed:cda/b aaaa=c,babbb=d magic:0
dc=1
cd=1
ca=ac
da=ad
aaaa=c
bcba=cbab
babaaa=dbcbc
bbbc=aaababb
babbd=adbbb
bbbac=aaababba
babbad=adbbba
bbbaac=aaababbaa
babbaad=adbbbaa
bbbaaa=aaadbbcb
babbaaa=dbbcbc
babbb=d
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 |
|---|
| 9 | 673 | ⟨a, b | aababbbaa=1⟩ | φ(a) = a, φ(b) = b |
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 | 648 | ⟨a, b | aaabbbaba=1⟩ | φ(a) = a, φ(b) = b |