#1364 ⟨a, b | aaababbbba=1⟩
Properties
- Presentation has sum-of-sides 10
- Infinite non-Abelian group
- Group inverses:
- a-1 = a3d
- b-1 = cbab3
- 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: aaaa=c
- Auxiliary generator: babbbb=d
- dc ⇒ 1
- cd ⇒ 1
- ca ⇒ ac
- da ⇒ ad
- a4 ⇒ c
- bcba ⇒ cbab
- baba3 ⇒ d(bc)2
- bab2a3 ⇒ db(bc)2
- b4c ⇒ a3bab3
- bab3d ⇒ adb4
- b4ac ⇒ a3bab3a
- bab3ad ⇒ adb4a
- b4a2c ⇒ a3bab3a2
- bab3a2d ⇒ adb4a2
- b4a3 ⇒ a3db3cb
- bab3a3 ⇒ db3cbc
- bab4 ⇒ d
# ab:aaababbbba=1 reversed:cda/b aaaa=c,babbbb=d magic:0
dc=1
cd=1
ca=ac
da=ad
aaaa=c
bcba=cbab
babaaa=dbcbc
babbaaa=dbbcbc
bbbbc=aaababbb
babbbd=adbbbb
bbbbac=aaababbba
babbbad=adbbbba
bbbbaac=aaababbbaa
babbbaad=adbbbbaa
bbbbaaa=aaadbbbcb
babbbaaa=dbbbcbc
babbbb=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 | 1434 | ⟨a, b | aababbbbaa=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.
1 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 1386 | ⟨a, b | aaabbbbaba=1⟩ | φ(a) = a, φ(b) = b |