#1378 ⟨a, b | aaabbbaaab=1⟩
Properties
- Presentation has sum-of-sides 10
- Infinite non-Abelian group
- Group inverses:
- a-1 = bdca2
- b-1 = bd2
- c-1 = d2
- d-1 = dc
Complete rewriting system
- Reduction order:
- Left-to-right recursive path with deg(d) = deg(c) = 0, d < c; deg(b) = deg(a) = 1, b < a
- Auxiliary generator: bb=c
- Auxiliary generator: aaab=d
- cd ⇒ dc
- d2c ⇒ 1
- cb ⇒ bc
- d2b ⇒ bd2
- b2 ⇒ c
- ab ⇒ bdcad
- adb ⇒ dbd2ac
- a3 ⇒ dbd2
# ab:aaabbbaaab=1 dc/ba bb=c,aaab=d frequency:2/1,4/0
cd=dc
ddc=1
cb=bc
ddb=bdd
bb=c
ab=bdcad
adb=dbddac
aaa=dbdd
Right Cayley graph (truncated)
Left Cayley graph (truncated)
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 |
|---|
| 10 | 1465 | ⟨a, b | aabbbabbba=1⟩ | φ(a) = b, φ(b) = a |