#1342 ⟨a, b | aaabaaabba=1⟩
Properties
- Presentation has sum-of-sides 10
- Infinite non-Abelian group
- Group inverses:
- a-1 = da3
- b-1 = bcba3
- c-1 = d
- d-1 = c
Complete rewriting system
- Reduction order:
- Left-to-right recursive path with deg(c) = deg(d) = deg(a) = 0, c < d < a; deg(b) = 1
- Auxiliary generator: aaaa=c
- Auxiliary generator: baaabb=d
- cd ⇒ 1
- dc ⇒ 1
- ac ⇒ ca
- ad ⇒ da
- a4 ⇒ c
- cba3b ⇒ bcba3
- dbcb ⇒ ba3bda
- abcb ⇒ cb2a
- aba3b ⇒ b2c
- a3b2 ⇒ bcbda3
- b2cb ⇒ da
- cba2b2 ⇒ (bc)2a2bd
- cbca2b2 ⇒ (bc)2a3bda3
- aba2b2 ⇒ b2ca3bd
- abca2b2 ⇒ b2c2bda3
# ab:aaabaaabba=1 cda/b aaaa=c,baaabb=d magic:0
cd=1
dc=1
ac=ca
ad=da
aaaa=c
cbaaab=bcbaaa
dbcb=baaabda
abcb=cbba
abaaab=bbc
aaabb=bcbdaaa
bbcb=da
cbaabb=bcbcaabd
cbcaabb=bcbcaaabdaaa
abaabb=bbcaaabd
abcaabb=bbccbdaaa
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.
3 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 1365 | ⟨a, b | aaabbaaaab=1⟩ | φ(a) = a, φ(b) = b |
| 10 | 1400 | ⟨a, b | aabaaabbaa=1⟩ | φ(a) = a, φ(b) = b |
| 10 | 1438 | ⟨a, b | aabbaaaaba=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 | 1366 | ⟨a, b | aaabbaaaba=1⟩ | φ(a) = a, φ(b) = b |
| 10 | 1396 | ⟨a, b | aabaaaabba=1⟩ | φ(a) = a, φ(b) = b |