#7795 ⟨a, b | aaa=1, abbab=ba⟩
Properties
- Presentation has sum-of-sides 10
- Finite non-commutative monoid with 129 elements
Element profile
- 2 element center:
- 2 idempotent elements:
Complete rewriting system
- Reduction order:
- Left-to-right recursive path with deg(a) = 0; deg(b) = 1
- a3 ⇒ 1
- b2ab ⇒ a2ba
- ab3 ⇒ (ba)3a
- (ab)2a2b ⇒ ba2b2a2
- (aba)2b ⇒ b(ba2)2
- ab(a2b)2 ⇒ bab2a
- a2b2a2b ⇒ ba2(ba)2
- a2bab2 ⇒ (ba2)3
- a(ab)3 ⇒ b3a
- (a2b)2b ⇒ b(aba)2
- (ba)2b2 ⇒ (aba)2
- ab2(a2b)2 ⇒ b2(a2b)2a
- abab2a2b ⇒ bab2a2ba
- b4a2b ⇒ aba2
- b3a2b2 ⇒ abab2a2
- (ab)5 ⇒ b5a2
- b7 ⇒ b
# ab:aaa=1,abbab=ba a/b
aaa=1
bbab=aaba
abbb=bababaa
ababaab=baabbaa
abaabab=bbaabaa
abaabaab=babba
aabbaab=baababa
aababb=baabaabaa
aababab=bbba
aabaabb=babaaba
bababb=abaaba
abbaabaab=bbaabaaba
ababbaab=babbaaba
bbbbaab=abaa
bbbaabb=ababbaa
ababababab=bbbbbaa
bbbbbbb=b
Right Cayley graph
Left Cayley graph
Other isomorphic instances
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
1 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 22259 | ⟨a, b | aaa=1, abaabb=ba⟩ | φ(a) = a, φ(b) = ab |
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 |
|---|
| 11 | 21691 | ⟨a, b | aaa=1, aababba=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 23308 | ⟨a, b | aaa=1, babb=abaa⟩ | φ(a) = a, φ(b) = b |