#304 ⟨a, b | aabaabba=1⟩
Properties
- Presentation has sum-of-sides 8
- Infinite non-Abelian group
- Group inverses:
- a-1 = da2
- b-1 = bcba2
- 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: aaa=c
- Auxiliary generator: baabb=d
- cd ⇒ 1
- dc ⇒ 1
- ac ⇒ ca
- ad ⇒ da
- a3 ⇒ c
- cba2b ⇒ bcba2
- dbcb ⇒ ba2bda
- abcb ⇒ cb2a
- aba2b ⇒ b2c
- a2b2 ⇒ bcbda2
- b2cb ⇒ da
- cbab2 ⇒ (bc)2abd
- cbcab2 ⇒ (bc)2a2bda2
- abab2 ⇒ b2ca2bd
- abcab2 ⇒ b2c2bda2
# ab:aabaabba=1 cda/b aaa=c,baabb=d magic:0
cd=1
dc=1
ac=ca
ad=da
aaa=c
cbaab=bcbaa
dbcb=baabda
abcb=cbba
abaab=bbc
aabb=bcbdaa
bbcb=da
cbabb=bcbcabd
cbcabb=bcbcaabdaa
ababb=bbcaabd
abcabb=bbccbdaa
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 |
|---|
| 8 | 311 | ⟨a, b | aabbaaab=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 |
|---|
| 8 | 312 | ⟨a, b | aabbaaba=1⟩ | φ(a) = a, φ(b) = b |
| 8 | 324 | ⟨a, b | abaaabba=1⟩ | φ(a) = a, φ(b) = b |