#6788 ⟨a, b | aba=b, baab=aa⟩

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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. a10 ⇒ a2
  2. ba8 ⇒ b
  3. ab ⇒ ba7
  4. b2 ⇒ a4 
# ab:aba=b,baab=aa a/b
aaaaaaaaaa=aa
baaaaaaaa=b
ab=baaaaaaa
bb=aaaa

Cayley table

Idempotents are shown in bold.

1aba2baa3ba2a4ba3a5ba4a6ba5a7ba6a8ba7a9
11aba2baa3ba2a4ba3a5ba4a6ba5a7ba6a8ba7a9
aaa2ba7a3ba4baa5ba2a6ba3a7ba4a8ba5a9ba6a2
bbbaa4ba2a5ba3a6ba4a7ba5a8ba6a9ba7a2ba3ba
a2a2a3ba6a4ba7a5ba6baa7ba2a8ba3a9ba4a2ba5a3
bababa2a3ba3a4ba4a5ba5a6ba6a7ba7a8ba9baa2ba2
a3a3a4ba5a5ba6a6ba7a7ba8baa9ba2a2ba3a3ba4a4
ba2ba2ba3a2ba4a3ba5a4ba6a5ba7a6ba7baa8ba2a9ba3
a4a4a5ba4a6ba5a7ba6a8ba7a9ba2baa3ba2a4ba3a5
ba3ba3ba4a9ba5a2ba6a3ba7a4ba5baa6ba2a7ba3a8ba4
a5a5a6ba3a7ba4a8ba5a9ba6a2ba7a3ba4baa5ba2a6
ba4ba4ba5a8ba6a9ba7a2ba3baa4ba2a5ba3a6ba4a7ba5
a6a6a7ba2a8ba3a9ba4a2ba5a3ba6a4ba7a5ba6baa7
ba5ba5ba6a7ba7a8ba9baa2ba2a3ba3a4ba4a5ba5a6ba6
a7a7a8baa9ba2a2ba3a3ba4a4ba5a5ba6a6ba7a7ba8
ba6ba6ba7a6ba7baa8ba2a9ba3a2ba4a3ba5a4ba6a5ba7
a8a8a9ba2baa3ba2a4ba3a5ba4a6ba5a7ba6a8ba7a9
ba7ba7ba5baa6ba2a7ba3a8ba4a9ba5a2ba6a3ba7a4b
a9a9a2ba7a3ba4baa5ba2a6ba3a7ba4a8ba5a9ba6a2

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
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
1116043⟨a, b | aaa=ab, bbbb=ba⟩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