#6795 ⟨a, b | aba=b, bbbb=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. b9 ⇒ b
  2. ba ⇒ ab5
  3. a2 ⇒ b4 
# ab:aba=b,bbbb=aa b/a
bbbbbbbbb=b
ba=abbbbb
aa=bbbb

Cayley table

Idempotents are shown in bold.

1ababb2ab2b3ab3b4ab4b5ab5b6ab6b7ab7b8ab8
11ababb2ab2b3ab3b4ab4b5ab5b6ab6b7ab7b8ab8
aab4abb5ab2b6ab3b7ab4b8ab5bab6b2ab7b3ab8b4
bbab5b2ab6b3ab7b4ab8b5abb6ab2b7ab3b8ab4bab5
ababbab2b2ab3b3ab4b4ab5b5ab6b6ab7b7ab8b8abb
b2b2ab2b3ab3b4ab4b5ab5b6ab6b7ab7b8ab8babb2ab2
ab2ab2b6ab3b7ab4b8ab5bab6b2ab7b3ab8b4abb5ab2b6
b3b3ab7b4ab8b5abb6ab2b7ab3b8ab4bab5b2ab6b3ab7
ab3ab3b3ab4b4ab5b5ab6b6ab7b7ab8b8abbab2b2ab3b3
b4b4ab4b5ab5b6ab6b7ab7b8ab8babb2ab2b3ab3b4ab4
ab4ab4b8ab5bab6b2ab7b3ab8b4abb5ab2b6ab3b7ab4b8
b5b5abb6ab2b7ab3b8ab4bab5b2ab6b3ab7b4ab8b5ab
ab5ab5b5ab6b6ab7b7ab8b8abbab2b2ab3b3ab4b4ab5b5
b6b6ab6b7ab7b8ab8babb2ab2b3ab3b4ab4b5ab5b6ab6
ab6ab6b2ab7b3ab8b4abb5ab2b6ab3b7ab4b8ab5bab6b2
b7b7ab3b8ab4bab5b2ab6b3ab7b4ab8b5abb6ab2b7ab3
ab7ab7b7ab8b8abbab2b2ab3b3ab4b4ab5b5ab6b6ab7b7
b8b8ab8babb2ab2b3ab3b4ab4b5ab5b6ab6b7ab7b8ab8
ab8ab8b4abb5ab2b6ab3b7ab4b8ab5bab6b2ab7b3ab8b4

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
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