#145 ⟨a, b | aababba=1⟩
Properties
- Presentation has sum-of-sides 7
- Infinite non-Abelian group
- Group inverses:
- a-1 = a2d
- 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: aaa=c
- Auxiliary generator: babb=d
- dc ⇒ 1
- cd ⇒ 1
- ca ⇒ ac
- da ⇒ ad
- a3 ⇒ c
- b2c ⇒ a(ab)2
- babd ⇒ adb2
- bcba ⇒ cbab
- b2ac ⇒ a2(ba)2
- (ba)2d ⇒ adb2a
- b2a2 ⇒ a2dbcb
- baba2 ⇒ d(bc)2
- bab2 ⇒ d
# ab:aababba=1 reversed:cda/b aaa=c,babb=d magic:0
dc=1
cd=1
ca=ac
da=ad
aaa=c
bbc=aabab
babd=adbb
bcba=cbab
bbac=aababa
babad=adbba
bbaa=aadbcb
babaa=dbcbc
babb=d
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.
2 total
| Σ | # | Presentation | Mapping |
|---|
| 7 | 147 | ⟨a, b | aabbaba=1⟩ | φ(a) = a, φ(b) = b |
| 7 | 157 | ⟨a, b | ababbba=1⟩ | φ(a) = b, φ(b) = a |