#16043 ⟨a, b | aaa=ab, bbbb=ba⟩

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Properties

Element profile

Complete rewriting system

Format:
Word to reduce:
Tips:
  • Lowercase letters stand for generators.
  • Spaces are ignored.
  • Numbers repeat the previous letter, e.g. b90.
Reduction strategy:
Path to normal form: 1 
1
  1. a9 ⇒ a4
  2. ba7 ⇒ ba2
  3. ab ⇒ a3
  4. b2a ⇒ ba3
  5. b4 ⇒ ba 
# ab:aaa=ab,bbbb=ba a/b
aaaaaaaaa=aaaa
baaaaaaa=baa
ab=aaa
bba=baaa
bbbb=ba

Cayley table

Idempotents are shown in bold.

1aba2bab2a3ba2b3a4ba3a5ba4a6ba5a7ba6a8
11aba2bab2a3ba2b3a4ba3a5ba4a6ba5a7ba6a8
aaa2a3a3a4a5a4a5a7a5a6a6a7a7a8a8a4a4
bbbab2ba2ba3b3ba3ba4baba4ba5ba5ba6ba6ba2ba2ba3ba3
a2a2a3a4a4a5a6a5a6a8a6a7a7a8a8a4a4a5a5
bababa2ba3ba3ba4ba5ba4ba5ba2ba5ba6ba6ba2ba2ba3ba3ba4ba4
b2b2ba3b3ba4ba5baba5ba6ba3ba6ba2ba2ba3ba3ba4ba4ba5ba5
a3a3a4a5a5a6a7a6a7a4a7a8a8a4a4a5a5a6a6
ba2ba2ba3ba4ba4ba5ba6ba5ba6ba3ba6ba2ba2ba3ba3ba4ba4ba5ba5
b3b3ba5baba6ba2ba3ba2ba3ba5ba3ba4ba4ba5ba5ba6ba6ba2ba2
a4a4a5a6a6a7a8a7a8a5a8a4a4a5a5a6a6a7a7
ba3ba3ba4ba5ba5ba6ba2ba6ba2ba4ba2ba3ba3ba4ba4ba5ba5ba6ba6
a5a5a6a7a7a8a4a8a4a6a4a5a5a6a6a7a7a8a8
ba4ba4ba5ba6ba6ba2ba3ba2ba3ba5ba3ba4ba4ba5ba5ba6ba6ba2ba2
a6a6a7a8a8a4a5a4a5a7a5a6a6a7a7a8a8a4a4
ba5ba5ba6ba2ba2ba3ba4ba3ba4ba6ba4ba5ba5ba6ba6ba2ba2ba3ba3
a7a7a8a4a4a5a6a5a6a8a6a7a7a8a8a4a4a5a5
ba6ba6ba2ba3ba3ba4ba5ba4ba5ba2ba5ba6ba6ba2ba2ba3ba3ba4ba4
a8a8a4a5a5a6a7a6a7a4a7a8a8a4a4a5a5a6a6

Right Cayley graph

Idempotents are shown in bold.

Left Cayley graph

Idempotents are shown in bold.

Others with same cardinality

17 unique, 104 total

Σ#PresentationDescriptionRelated
81121⟨a, b | aa=1, abbba=b⟩Finite non-commutative monoid with 18 elements17 iso
93387⟨a, b | aa=1, abbbbb=b⟩Finite non-commutative monoid with 18 elements22 iso, 9 anti-iso
105521⟨a, b | aaab=1, bbbbbb=1⟩Isomorphic to ℤ1833 iso
106732⟨a, b | aba=a, aaab=bb⟩Finite non-commutative monoid with 18 elements
106788⟨a, b | aba=b, baab=aa⟩Finite non-commutative monoid with 18 elements
106795⟨a, b | aba=b, bbbb=aa⟩Finite non-commutative monoid with 18 elements
107039⟨a, b | bb=aa, aaaba=b⟩Finite non-commutative monoid with 18 elements2 iso
108910⟨a, b | aa=a, bbbbb=ab⟩Finite non-commutative monoid with 18 elements1 iso
1112187⟨a, b | aaaa=ab, babb=b⟩Finite non-commutative monoid with 18 elements2 iso
1115797⟨a, b | aab=bb, bbbba=a⟩Finite non-commutative monoid with 18 elements
1116042⟨a, b | aaa=ab, bbbb=ab⟩Finite non-commutative monoid with 18 elements
1116313⟨a, b | aab=bb, baba=aa⟩Finite non-commutative monoid with 18 elements
1118758⟨a, b | aaa=a, bbbbbb=a⟩Isomorphic to ℕ(18 = 6)
1118830⟨a, b | aaa=b, bbbbbb=a⟩Isomorphic to ℕ(18 = 1)
1118831⟨a, b | aaa=b, bbbbbb=b⟩Isomorphic to ℕ(18 = 3)
1119624⟨a, b | aab=b, bbbba=aa⟩Finite non-commutative monoid with 18 elements
1120914⟨a, b | bb=aa, ababa=aa⟩Finite non-commutative monoid with 18 elements1 iso