#645 ⟨a, b | aaabbabba=1⟩
Properties
- Presentation has sum-of-sides 9
- Infinite non-Abelian group
- Group inverses:
- a-1 = da3
- b-1 = ba4ca
- c-1 = a4ca
- d-1 = a4
Complete rewriting system
- Reduction order:
- Right-to-left recursive path with deg(a) = deg(d) = 0, a < d; deg(c) = deg(b) = 1, c < b
- Auxiliary generator: bb=c
- Auxiliary generator: cac=d
- ad ⇒ da
- da4 ⇒ 1
- ca2 ⇒ a6cd
- cda ⇒ dac
- cd2 ⇒ d3a3ca
- cac ⇒ d
- cb ⇒ bc
- cab ⇒ dba4ca
- b2 ⇒ c
# ab:aaabbabba=1 reversed:ad/cb bb=c,cac=d frequency:2/0,3/2
ad=da
daaaa=1
caa=aaaaaacd
cda=dac
cdd=dddaaaca
cac=d
cb=bc
cab=dbaaaaca
bb=c
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 |
|---|
| 9 | 690 | ⟨a, b | aabbbbaab=1⟩ | φ(a) = b, φ(b) = a |
| 9 | 709 | ⟨a, b | abaabbbba=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.
1 total
| Σ | # | Presentation | Mapping |
|---|
| 9 | 683 | ⟨a, b | aabbabbaa=1⟩ | φ(a) = a, φ(b) = b |