#670 ⟨a, b | aabababba=1⟩
Properties
- Presentation has sum-of-sides 9
- Infinite non-Abelian group
- Group inverses:
- a-1 = a2d
- b-1 = cb(ab)2
- 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: bababb=d
- dc ⇒ 1
- cd ⇒ 1
- ca ⇒ ac
- da ⇒ ad
- a3 ⇒ c
- bcba ⇒ ab2c
- b2a2 ⇒ a2dbcb
- bab2c ⇒ a(ab)3
- b(ab)2d ⇒ adbab2
- bab2ac ⇒ a2(ba)3
- (ba)3d ⇒ adbab2a
- (ba)3a ⇒ adb(bc)2
- (ba)2b2 ⇒ d
- (b2c)2 ⇒ a2dba2cb(ab)2
- b2cb2ac ⇒ a2dba2c(ba)3
# ab:aabababba=1 reversed:cda/b aaa=c,bababb=d magic:0
dc=1
cd=1
ca=ac
da=ad
aaa=c
bcba=abbc
bbaa=aadbcb
babbc=aababab
bababd=adbabb
babbac=aabababa
bababad=adbabba
bababaa=adbbcbc
bababb=d
bbcbbc=aadbaacbabab
bbcbbac=aadbaacbababa
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 | 716 | ⟨a, b | ababbaaab=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.
2 total
| Σ | # | Presentation | Mapping |
|---|
| 9 | 682 | ⟨a, b | aabbababa=1⟩ | φ(a) = a, φ(b) = b |
| 9 | 715 | ⟨a, b | abababbba=1⟩ | φ(a) = b, φ(b) = a |