#1297 ⟨a, b | aaaaababba=1⟩
Properties
- Presentation has sum-of-sides 10
- Infinite non-Abelian group
- Group inverses:
- a-1 = a5d
- 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: aaaaaa=c
- Auxiliary generator: babb=d
- dc ⇒ 1
- cd ⇒ 1
- ca ⇒ ac
- da ⇒ ad
- a6 ⇒ c
- b2c ⇒ a5bab
- babd ⇒ adb2
- bcba ⇒ cbab
- b2ac ⇒ a5(ba)2
- (ba)2d ⇒ adb2a
- b2a2c ⇒ a5baba2
- baba2d ⇒ adb2a2
- b2a3c ⇒ a5baba3
- baba3d ⇒ adb2a3
- b2a4c ⇒ a5baba4
- baba4d ⇒ adb2a4
- b2a5 ⇒ a5dbcb
- baba5 ⇒ d(bc)2
- bab2 ⇒ d
# ab:aaaaababba=1 reversed:cda/b aaaaaa=c,babb=d magic:0
dc=1
cd=1
ca=ac
da=ad
aaaaaa=c
bbc=aaaaabab
babd=adbb
bcba=cbab
bbac=aaaaababa
babad=adbba
bbaac=aaaaababaa
babaad=adbbaa
bbaaac=aaaaababaaa
babaaad=adbbaaa
bbaaaac=aaaaababaaaa
babaaaad=adbbaaaa
bbaaaaa=aaaaadbcb
babaaaaa=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.
2 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 1318 | ⟨a, b | aaaababbaa=1⟩ | φ(a) = a, φ(b) = b |
| 10 | 1358 | ⟨a, b | aaababbaaa=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 |
|---|
| 10 | 1301 | ⟨a, b | aaaaabbaba=1⟩ | φ(a) = a, φ(b) = b |
| 10 | 1326 | ⟨a, b | aaaabbabaa=1⟩ | φ(a) = a, φ(b) = b |
| 10 | 1526 | ⟨a, b | ababbbbbba=1⟩ | φ(a) = b, φ(b) = a |