#1312 ⟨a, b | aaaabaabba=1⟩
Properties
- Presentation has sum-of-sides 10
- Infinite non-Abelian group
- Group inverses:
- a-1 = a4d
- b-1 = cba2b
- c-1 = d
- d-1 = c
Complete rewriting system
- Reduction order:
- Right-to-left recursive path with deg(c) = deg(d) = deg(a) = 0, c < d < a; deg(b) = 1
- Auxiliary generator: aaaaa=c
- Auxiliary generator: baabb=d
- dc ⇒ 1
- cd ⇒ 1
- ca ⇒ ac
- da ⇒ ad
- a5 ⇒ c
- b2c ⇒ a(a2b)2
- ba2bd ⇒ a2db2
- b2ac ⇒ a(a2b)2a
- ba2bad ⇒ a2db2a
- bcba2 ⇒ cba2b
- b2a2c ⇒ a3(ba2)2
- (ba2)2d ⇒ a2db2a2
- b2a3 ⇒ a3dbcb
- ba2ba3 ⇒ d(bc)2
- ba2b2 ⇒ d
# ab:aaaabaabba=1 reversed:cda/b aaaaa=c,baabb=d magic:0
dc=1
cd=1
ca=ac
da=ad
aaaaa=c
bbc=aaabaab
baabd=aadbb
bbac=aaabaaba
baabad=aadbba
bcbaa=cbaab
bbaac=aaabaabaa
baabaad=aadbbaa
bbaaa=aaadbcb
baabaaa=dbcbc
baabb=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.
1 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 1348 | ⟨a, b | aaabaabbaa=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.
3 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 1324 | ⟨a, b | aaaabbaaba=1⟩ | φ(a) = a, φ(b) = b |
| 10 | 1368 | ⟨a, b | aaabbaabaa=1⟩ | φ(a) = a, φ(b) = b |
| 10 | 1540 | ⟨a, b | abbabbbbba=1⟩ | φ(a) = b, φ(b) = a |