#1427 ⟨a, b | aababbaaba=1⟩
Properties
- Presentation has sum-of-sides 10
- Infinite non-Abelian group
- Group inverses:
- a-1 = adac
- b-1 = ba2da
- c-1 = a2da
- d-1 = aca2
Complete rewriting system
- Reduction order:
- Left-to-right recursive path with deg(a) = deg(c) = deg(d) = 0, a < c < d; deg(b) = 1
- Auxiliary generator: bb=c
- Auxiliary generator: baaab=d
- ca2d ⇒ adac
- daca ⇒ adac
- a2dac ⇒ 1
- cb ⇒ bc
- db ⇒ ba3c
- dab ⇒ abaca2
- a3b ⇒ ba(ad)2
- ca2b ⇒ a2bacadac
- b2 ⇒ c
# ab:aababbaaba=1 acd/b bb=c,baaab=d frequency:2/3,5/2
caad=adac
daca=adac
aadac=1
cb=bc
db=baaac
dab=abacaa
aaab=baadad
caab=aabacadac
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.
1 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 1486 | ⟨a, b | abaaababba=1⟩ | φ(a) = a, φ(b) = b |