#1350 ⟨a, b | aaabaabbba=1⟩
Properties
- Presentation has sum-of-sides 10
- Infinite non-Abelian group
- Group inverses:
- a-1 = a3ba2c
- b-1 = db2
- c-1 = d
- d-1 = c
Complete rewriting system
- Reduction order:
- Left-to-right recursive path with deg(c) = deg(d) = deg(b) = 0, c < d < b; deg(a) = 1
- Auxiliary generator: bbb=c
- Auxiliary generator: aaaabaa=d
- cd ⇒ 1
- dc ⇒ 1
- bc ⇒ cb
- bd ⇒ db
- b3 ⇒ c
- ba2ca ⇒ aba2c
- b2aba2 ⇒ ca2cad
- ca4 ⇒ (a2b)2b
- da2ba2 ⇒ a4db
- cba4 ⇒ (ba2)2b2
- d(ba2)2 ⇒ ba4db
- b2a4 ⇒ a2ca2db2
- b(ba2)2 ⇒ (ca2)2d
- da3ba2 ⇒ a4bad
- dba3ba2 ⇒ ba4bad
- b2a3ba2 ⇒ ca2ca3d
- a4ba2 ⇒ d
# ab:aaabaabbba=1 cdb/a bbb=c,aaaabaa=d magic:1
cd=1
dc=1
bc=cb
bd=db
bbb=c
baaca=abaac
bbabaa=caacad
caaaa=aabaabb
daabaa=aaaadb
cbaaaa=baabaabb
dbaabaa=baaaadb
bbaaaa=aacaadbb
bbaabaa=caacaad
daaabaa=aaaabad
dbaaabaa=baaaabad
bbaaabaa=caacaaad
aaaabaa=d
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 |
|---|
| 10 | 1412 | ⟨a, b | aabaabbbaa=1⟩ | φ(a) = a, φ(b) = b |
| 10 | 1469 | ⟨a, b | aabbbbabba=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.
2 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 1379 | ⟨a, b | aaabbbaaba=1⟩ | φ(a) = a, φ(b) = b |
| 10 | 1456 | ⟨a, b | aabbabbbba=1⟩ | φ(a) = b, φ(b) = a |