#1377 ⟨a, b | aaabbabbba=1⟩
Properties
- Presentation has sum-of-sides 10
- Infinite non-Abelian group
- Group inverses:
- a-1 = a3d
- b-1 = cb2ab2
- 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: bbabbb=d
- dc ⇒ 1
- cd ⇒ 1
- ca ⇒ ac
- da ⇒ ad
- a4 ⇒ c
- b3c ⇒ a3b2ab
- b2abd ⇒ adb3
- bcb2a ⇒ cb2ab
- b3ac ⇒ a3b(ba)2
- b(ba)2d ⇒ adb3a
- b3a2c ⇒ a3b2aba2
- b2aba2d ⇒ adb3a2
- b3a3 ⇒ a3dbcb2
- b2aba3 ⇒ dbcb2c
- b2ab2d ⇒ dbab3
- (b2a)2d ⇒ dbab3a
- (b2a)2ad ⇒ dbab3a2
- b2ab2a3 ⇒ d(b2c)2
- b2ab3 ⇒ d
# ab:aaabbabbba=1 reversed:cda/b aaaa=c,bbabbb=d magic:0
dc=1
cd=1
ca=ac
da=ad
aaaa=c
bbbc=aaabbab
bbabd=adbbb
bcbba=cbbab
bbbac=aaabbaba
bbabad=adbbba
bbbaac=aaabbabaa
bbabaad=adbbbaa
bbbaaa=aaadbcbb
bbabaaa=dbcbbc
bbabbd=dbabbb
bbabbad=dbabbba
bbabbaad=dbabbbaa
bbabbaaa=dbbcbbc
bbabbb=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 | 1454 | ⟨a, b | aabbabbbaa=1⟩ | φ(a) = a, φ(b) = b |
| 10 | 1467 | ⟨a, b | aabbbbaaba=1⟩ | φ(a) = b, φ(b) = a |
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 | 1383 | ⟨a, b | aaabbbabba=1⟩ | φ(a) = a, φ(b) = b |
| 10 | 1414 | ⟨a, b | aabaabbbba=1⟩ | φ(a) = b, φ(b) = a |