#16545 ⟨a, b | aba=bb, abb=aaa⟩

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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. a6 ⇒ a4
  2. a4b ⇒ a4
  3. a2ba ⇒ a3
  4. ba4 ⇒ a4
  5. b2 ⇒ aba
  6. ba3b ⇒ a5
  7. (ba)2 ⇒ (ab)2 
# ab:aba=bb,abb=aaa reversed:a/b
aaaaaa=aaaa
aaaab=aaaa
aaba=aaa
baaaa=aaaa
bb=aba
baaab=aaaaa
baba=abab

Cayley table

Idempotents are shown in bold.

1aba2abbaa3a2bababa2baba4a3baba2(ab)2ba3ba2ba5aba3aba2b
11aba2abbaa3a2bababa2baba4a3baba2(ab)2ba3ba2ba5aba3aba2b
aaa2aba3a2babaa4a3ba3aba2(ab)2a5a4a4a3baba3aba2ba4a5a4
bbbaababa2bababa2ba3ba2b(ab)2aba3aba2ba4a5a3baba3a5a4a5a4a5
a2a2a3a2ba4a3ba3a5a4a4a4a3ba4a5a5a4a5a4a5a4a5
abababaa3aba2(ab)2a4aba3aba2ba3ba5a4a5a4a4a5a4a5a4a5a4
bababa2babba3ba2b(ab)2a4a5ba3a3baba3a5a4a4a5a4a5a4a5a4
a3a3a4a3ba5a4a4a4a5a5a5a4a5a4a4a5a4a5a4a5a4
a2ba2ba3a4a4a3ba5a5a4a4a4a5a4a5a5a4a5a4a5a4a5
abaabaaba2(ab)2aba3aba2ba3ba5a4aba3a4a5a4a5a5a4a5a4a5a4a5
ba2ba2ba3ba2ba4a5ba3a5a4a4a4a5a4a5a5a4a5a4a5a4a5
babbab(ab)2ba3a3baba3a4a4a5a5a5a4a5a4a4a5a4a5a4a5a4
a4a4a5a4a4a5a5a5a4a4a4a5a4a5a5a4a5a4a5a4a5
a3ba3ba4a5a5a4a4a4a5a5a5a4a5a4a4a5a4a5a4a5a4
aba2aba2aba3aba2ba5a4aba3a4a5a5a5a4a5a4a4a5a4a5a4a5a4
(ab)2(ab)2a3baba3a4a5a5a5a4a4a4a5a4a5a5a4a5a4a5a4a5
ba3ba3a4a5a5a4a4a4a5a5a5a4a5a4a4a5a4a5a4a5a4
ba2bba2bba3a4a4a5a5a5a4a4a4a5a4a5a5a4a5a4a5a4a5
a5a5a4a5a5a4a4a4a5a5a5a4a5a4a4a5a4a5a4a5a4
aba3aba3a5a4a4a5a5a5a4a4a4a5a4a5a5a4a5a4a5a4a5
aba2baba2baba3a5a5a4a4a4a5a5a5a4a5a4a4a5a4a5a4a5a4

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
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
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