#12159 ⟨a, b | aaaa=aa, abbb=b⟩

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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. b5 ⇒ b
  2. ab ⇒ b3
  3. a4 ⇒ a2 
# ab:aaaa=aa,abbb=b b/a
bbbbb=b
ab=bbb
aaaa=aa

Cayley table

Idempotents are shown in bold.

1aba2bab2a3ba2b2ab3ba3b2a2b3ab4b2a3b3a2b4ab3a3b4a2b4a3
11aba2bab2a3ba2b2ab3ba3b2a2b3ab4b2a3b3a2b4ab3a3b4a2b4a3
aaa2b3a3b3ab4a2b3a2b4abb3a3b4a2bab2b4a3ba2b2aba3b2a2b2a3
bbbab2ba2b2ab3ba3b2a2b3ab4b2a3b3a2b4abb3a3b4a2bab4a3ba2ba3
a2a2a3ba2bab2a3ba2b2ab3ba3b2a2b3ab4b2a3b3a2b4ab3a3b4a2b4a3
bababa2b4ba3b4abba2b4a2bab2b4a3ba2b2ab3ba3b2a2b3ab2a3b3a2b3a3
b2b2b2ab3b2a2b3ab4b2a3b3a2b4abb3a3b4a2bab2b4a3ba2b2aba3b2a2b2a3
a3a3a2b3a3b3ab4a2b3a2b4abb3a3b4a2bab2b4a3ba2b2aba3b2a2b2a3
ba2ba2ba3b2ba2b2ab3ba3b2a2b3ab4b2a3b3a2b4abb3a3b4a2bab4a3ba2ba3
b2ab2ab2a2bb2a3bab2b2a2ba2b2ab3ba3b2a2b3ab4b2a3b3a2b4ab3a3b4a2b4a3
b3b3b3ab4b3a2b4abb3a3b4a2bab2b4a3ba2b2ab3ba3b2a2b3ab2a3b3a2b3a3
ba3ba3ba2b4ba3b4abba2b4a2bab2b4a3ba2b2ab3ba3b2a2b3ab2a3b3a2b3a3
b2a2b2a2b2a3b3b2a2b3ab4b2a3b3a2b4abb3a3b4a2bab2b4a3ba2b2aba3b2a2b2a3
b3ab3ab3a2b2b3a3b2ab3b3a2b2a2b3ab4b2a3b3a2b4abb3a3b4a2bab4a3ba2ba3
b4b4b4abb4a2bab2b4a3ba2b2ab3ba3b2a2b3ab4b2a3b3a2b4ab3a3b4a2b4a3
b2a3b2a3b2a2bb2a3bab2b2a2ba2b2ab3ba3b2a2b3ab4b2a3b3a2b4ab3a3b4a2b4a3
b3a2b3a2b3a3b4b3a2b4abb3a3b4a2bab2b4a3ba2b2ab3ba3b2a2b3ab2a3b3a2b3a3
b4ab4ab4a2b3b4a3b3ab4b4a2b3a2b4abb3a3b4a2bab2b4a3ba2b2aba3b2a2b2a3
b3a3b3a3b3a2b2b3a3b2ab3b3a2b2a2b3ab4b2a3b3a2b4abb3a3b4a2bab4a3ba2ba3
b4a2b4a2b4a3bb4a2bab2b4a3ba2b2ab3ba3b2a2b3ab4b2a3b3a2b4ab3a3b4a2b4a3
b4a3b4a3b4a2b3b4a3b3ab4b4a2b3a2b4abb3a3b4a2bab2b4a3ba2b2aba3b2a2b2a3

Right Cayley graph

Idempotents are shown in bold.

Left Cayley graph

Idempotents are shown in bold.

Others with same cardinality

20 unique, 65 total

Σ#PresentationDescriptionRelated
8526⟨a, b | aab=a, bbbb=1⟩Finite non-commutative monoid with 20 elements10 iso, 9 anti-iso
92207⟨a, b | ab=aa, bbbb=b⟩Finite non-commutative monoid with 20 elements1 anti-iso
104095⟨a, b | baa=abb, abab=1⟩Finite non-Abelian group with 20 elements4 iso, 1 anti-iso
104212⟨a, b | aaaaa=1, abbbb=1⟩Isomorphic to ℤ2016 iso
105349⟨a, b | aaa=bb, bab=aa⟩Finite non-commutative monoid with 20 elements1 iso
106728⟨a, b | aba=a, aaaa=bb⟩Finite non-commutative monoid with 20 elements
106764⟨a, b | aba=b, aaaa=bb⟩Finite non-commutative monoid with 20 elements
107117⟨a, b | ab=aa, bbbb=bb⟩Finite non-commutative monoid with 20 elements
1112322⟨a, b | aaab=bb, bbba=a⟩Finite non-commutative monoid with 20 elements
1114367⟨a, b | aaaa=a, bbbbb=a⟩Isomorphic to ℕ(20 = 5)
1114407⟨a, b | aaaa=b, bbbbb=a⟩Isomorphic to ℕ(20 = 1)
1114408⟨a, b | aaaa=b, bbbbb=b⟩Isomorphic to ℕ(20 = 4)
1115933⟨a, b | aba=bb, baaab=a⟩Finite non-commutative monoid with 20 elements
1116124⟨a, b | aab=aa, baba=bb⟩Finite non-commutative monoid with 20 elements
1116339⟨a, b | aba=aa, aaaa=bb⟩Finite non-commutative monoid with 20 elements
1116343⟨a, b | aba=aa, aaab=bb⟩Finite non-commutative monoid with 20 elements
1116545⟨a, b | aba=bb, abb=aaa⟩Finite non-commutative monoid with 20 elements
1118619⟨a, b | aba=b, aaaaabb=1⟩Finite non-Abelian group with 20 elements3 iso
1119503⟨a, b | aab=a, bbbbb=bb⟩Finite non-commutative monoid with 20 elements
1121047⟨a, b | ab=aa, bbbb=bbb⟩Finite non-commutative monoid with 20 elements