#617 ⟨a, b | aaaababba=1⟩
Properties
- Presentation has sum-of-sides 9
- Infinite non-Abelian group
- Group inverses:
- a-1 = a4d
- b-1 = cbab
- 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: aaaaa=c
- Auxiliary generator: babb=d
- dc ⇒ 1
- cd ⇒ 1
- ca ⇒ ac
- da ⇒ ad
- a5 ⇒ c
- b2c ⇒ a4bab
- babd ⇒ adb2
- bcba ⇒ cbab
- b2ac ⇒ a4(ba)2
- (ba)2d ⇒ adb2a
- b2a2c ⇒ a4baba2
- baba2d ⇒ adb2a2
- b2a3c ⇒ a4baba3
- baba3d ⇒ adb2a3
- b2a4 ⇒ a4dbcb
- baba4 ⇒ d(bc)2
- bab2 ⇒ d
# ab:aaaababba=1 reversed:cda/b aaaaa=c,babb=d magic:0
dc=1
cd=1
ca=ac
da=ad
aaaaa=c
bbc=aaaabab
babd=adbb
bcba=cbab
bbac=aaaababa
babad=adbba
bbaac=aaaababaa
babaad=adbbaa
bbaaac=aaaababaaa
babaaad=adbbaaa
bbaaaa=aaaadbcb
babaaaa=dbcbc
babb=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 | 637 | ⟨a, b | aaababbaa=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.
3 total
| Σ | # | Presentation | Mapping |
|---|
| 9 | 621 | ⟨a, b | aaaabbaba=1⟩ | φ(a) = a, φ(b) = b |
| 9 | 643 | ⟨a, b | aaabbabaa=1⟩ | φ(a) = a, φ(b) = b |
| 9 | 720 | ⟨a, b | ababbbbba=1⟩ | φ(a) = b, φ(b) = a |