#1320 ⟨a, b | aaaababbba=1⟩
Properties
- Presentation has sum-of-sides 10
- Infinite non-Abelian group
- Group inverses:
- a-1 = a4d
- 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: aaaaa=c
- Auxiliary generator: babbb=d
- dc ⇒ 1
- cd ⇒ 1
- ca ⇒ ac
- da ⇒ ad
- a5 ⇒ c
- bcba ⇒ cbab
- baba4 ⇒ d(bc)2
- b3c ⇒ a4bab2
- bab2d ⇒ adb3
- b3ac ⇒ a4bab2a
- bab2ad ⇒ adb3a
- b3a2c ⇒ a4bab2a2
- bab2a2d ⇒ adb3a2
- b3a3c ⇒ a4bab2a3
- bab2a3d ⇒ adb3a3
- b3a4 ⇒ a4db2cb
- bab2a4 ⇒ db(bc)2
- bab3 ⇒ d
# ab:aaaababbba=1 reversed:cda/b aaaaa=c,babbb=d magic:0
dc=1
cd=1
ca=ac
da=ad
aaaaa=c
bcba=cbab
babaaaa=dbcbc
bbbc=aaaababb
babbd=adbbb
bbbac=aaaababba
babbad=adbbba
bbbaac=aaaababbaa
babbaad=adbbbaa
bbbaaac=aaaababbaaa
babbaaad=adbbbaaa
bbbaaaa=aaaadbbcb
babbaaaa=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 |
|---|
| 10 | 1362 | ⟨a, b | aaababbbaa=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 |
|---|
| 10 | 1332 | ⟨a, b | aaaabbbaba=1⟩ | φ(a) = a, φ(b) = b |
| 10 | 1381 | ⟨a, b | aaabbbabaa=1⟩ | φ(a) = a, φ(b) = b |