#6732 ⟨a, b | aba=a, aaab=bb⟩

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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. a7 ⇒ a3
  2. ba3 ⇒ a6
  3. aba ⇒ a
  4. b2 ⇒ a3b 
# ab:aba=a,aaab=bb a/b
aaaaaaa=aaa
baaa=aaaaaa
aba=a
bb=aaab

Cayley table

Idempotents are shown in bold.

1aba2abbaa3a2bba2baba4a3bba2ba5a4ba6a5ba6b
11aba2abbaa3a2bba2baba4a3bba2ba5a4ba6a5ba6b
aaa2aba3a2baa4a3ba2aba5a4ba2ba6a5ba3a6ba3b
bbbaa3bba2baba3a6ba2ba4a3ba3a6ba4ba4a3ba5a4ba5b
a2a2a3a2ba4a3ba2a5a4ba3a2ba6a5ba3ba3a6ba4a3ba4b
ababaa4ba2aba4a3a2ba5a4ba4a3ba5ba5a4ba6a5ba6b
bababa2baba6ba2bbaa3a6bba2baba4a3bba2ba5a4ba6a5ba6b
a3a3a4a3ba5a4ba3a6a5ba4a3ba3a6ba4ba4a3ba5a4ba5b
a2ba2ba2a5ba3a2ba5a4a3ba6a5ba5a4ba6ba6a5ba3a6ba3b
ba2ba2a6ba2ba3a6bba2a4a3ba6ba2ba5a4ba6ba6a5ba3a6ba3b
babbabbaa3bba2baba3a6ba2ba4a3ba3a6ba4ba4a3ba5a4ba5b
a4a4a5a4ba6a5ba4a3a6ba5a4ba4a3ba5ba5a4ba6a5ba6b
a3ba3ba3a6ba4a3ba6a5a4ba3a6ba6a5ba3ba3a6ba4a3ba4b
ba2bba2bba2a4ba6ba2ba4a3a6ba5a4ba4a3ba5ba5a4ba6a5ba6b
a5a5a6a5ba3a6ba5a4a3ba6a5ba5a4ba6ba6a5ba3a6ba3b
a4ba4ba4a3ba5a4ba3a6a5ba4a3ba3a6ba4ba4a3ba5a4ba5b
a6a6a3a6ba4a3ba6a5a4ba3a6ba6a5ba3ba3a6ba4a3ba4b
a5ba5ba5a4ba6a5ba4a3a6ba5a4ba4a3ba5ba5a4ba6a5ba6b
a6ba6ba6a5ba3a6ba5a4a3ba6a5ba5a4ba6ba6a5ba3a6ba3b

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
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
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