#5349 ⟨a, b | aaa=bb, bab=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 ⇒ a4
  2. ba8 ⇒ ba2
  3. aba2 ⇒ ba7
  4. a2b ⇒ ba4
  5. b2 ⇒ a3
  6. bab ⇒ a2 
# ab:aaa=bb,bab=aa a/b
aaaaaaaaaa=aaaa
baaaaaaaa=baa
abaa=baaaaaaa
aab=baaaa
bb=aaa
bab=aa

Cayley table

Idempotents are shown in bold.

1aba2abbaa3ababa2a4ba3a5ba4a6ba5a7ba6a8ba7a9
11aba2abbaa3ababa2a4ba3a5ba4a6ba5a7ba6a8ba7a9
aaa2aba3ba4abaa4ba5ba7a5ba2a6ba3a7ba4a8ba5a9ba6a4
bbbaa3ba2a2a4ba3a3a5ba4a6ba5a7ba6a8ba7a9ba2a4ba3
a2a2a3ba4a4ba3ba5a5ba4ba6a6ba7a7ba2a8ba3a9ba4a4ba5a5
abababaa4ba7a3a5ba2a4a6ba3a7ba4a8ba5a9ba6a4ba7a5ba2
bababa2a2ba3a7a3ba4a8a4ba5a5ba6a6ba7a7ba2a8ba3a9ba4
a3a3a4ba3a5ba2ba4a6ba3ba5a7ba6a8ba7a9ba2a4ba3a5ba4a6
abaababa7a3ba2a8a4ba3a9a5ba4a6ba5a7ba6a8ba7a9ba2a4ba3
ba2ba2ba3a7ba4a6a8ba5a7a9ba6a4ba7a5ba2a6ba3a7ba4a8ba5
a4a4a5ba2a6ba7ba3a7ba2ba4a8ba5a9ba6a4ba7a5ba2a6ba3a7
ba3ba3ba4a6ba5a5a7ba6a6a8ba7a9ba2a4ba3a5ba4a6ba5a7ba6
a5a5a6ba7a7ba6ba2a8ba7ba3a9ba4a4ba5a5ba6a6ba7a7ba2a8
ba4ba4ba5a5ba6a4a6ba7a5a7ba2a8ba3a9ba4a4ba5a5ba6a6ba7
a6a6a7ba6a8ba5ba7a9ba6ba2a4ba3a5ba4a6ba5a7ba6a8ba7a9
ba5ba5ba6a4ba7a9a5ba2a4a6ba3a7ba4a8ba5a9ba6a4ba7a5ba2
a7a7a8ba5a9ba4ba6a4ba5ba7a5ba2a6ba3a7ba4a8ba5a9ba6a4
ba6ba6ba7a9ba2a8a4ba3a9a5ba4a6ba5a7ba6a8ba7a9ba2a4ba3
a8a8a9ba4a4ba3ba5a5ba4ba6a6ba7a7ba2a8ba3a9ba4a4ba5a5
ba7ba7ba2a8ba3a7a9ba4a8a4ba5a5ba6a6ba7a7ba2a8ba3a9ba4
a9a9a4ba3a5ba2ba4a6ba3ba5a7ba6a8ba7a9ba2a4ba3a5ba4a6

Right Cayley graph

Idempotents are shown in bold.

Left Cayley graph

Idempotents are shown in bold.

Others with same cardinality

20 unique, 64 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
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
1112159⟨a, b | aaaa=aa, abbb=b⟩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

Other isomorphic instances

The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.

1 total

Σ#PresentationMapping
1116452⟨a, b | aba=bb, abab=aa⟩φ(a) = b, φ(b) = a