#15933 ⟨a, b | aba=bb, baaab=a⟩

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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 ⇒ a
  2. aba6 ⇒ ab
  3. a2b ⇒ ba2
  4. b2 ⇒ aba
  5. bab ⇒ a5 
# ab:aba=bb,baaab=a a/b
aaaaaaa=a
abaaaaaa=ab
aab=baa
bb=aba
bab=aaaaa

Cayley table

Idempotents are shown in bold.

1aba2abbaa3ababa2a4aba2ba3a5aba3ba4a6aba4ba5aba5ba6
11aba2abbaa3ababa2a4aba2ba3a5aba3ba4a6aba4ba5aba5ba6
aaa2aba3ba2abaa4ba3aba2a5ba4aba3a6ba5aba4aba6aba5baab
bbbaababa2a5aba2ba3a6aba3ba4aaba4ba5a2aba5ba6a3aba4aba
a2a2a3ba2a4aba2ba3a5aba3ba4a6aba4ba5aaba5ba6a2abbaababa2
ababababa3aba2a6ba4aba3aba5aba4a2ba6aba5a3baaba4ba2a5ba3
bababa2a5ba3aba3a6ba4aba4aba5aba5a2ba6aba3baabaa4aba2a5
a3a3a4aba2a5ba4aba3a6ba5aba4aba6aba5a2baaba3ba2ababa3aba2
abaabaaba2a6aba3ba5aaba4ba6a2aba5baa3abba2a4ababa3a5ba4a6
ba2ba2ba3aba3ba4aaba4ba5a2aba5ba6a3abbaa4ababa2a5aba2a6aba3
a4a4a5ba4a6aba4ba5aaba5ba6a2abbaa3ababa2a4aba2ba3aba3ba4
aba2aba2aba3ba5aba4a2ba6aba5a3baaba4ba2abaa5ba3aba2a6ba4aba5
ba3ba3ba4aba5aba5a2ba6aba3baabaa4ba2aba2a5ba3aba3a6aba4a
a5a5a6aba4aba6aba5a2baaba3ba2abaa4ba3aba2a5ba4aba3ba5aba4
aba3aba3aba4a2aba5baa3abba2a4ababa3a5aba2ba4a6aba3ba5aba6a2
ba4ba4ba5aba5ba6a3abbaa4ababa2a5aba2ba3a6aba3ba4aaba4a2aba5
a6a6aba6a2abbaa3ababa2a4aba2ba3a5aba3ba4a6aba4ba5aba5ba6
aba4aba4aba5baaba4ba2abaa5ba3aba2a6ba4aba3aba5aba4a2ba6a3ba
ba5ba5ba6a3baabaa4ba2aba2a5ba3aba3a6ba4aba4aba5aba5a2aba3
aba5aba5aba4ababa3a5aba2ba4a6aba3ba5aaba4ba6a2aba5baa3ba2a4
ba6ba6baababa2a5aba2ba3a6aba3ba4aaba4ba5a2aba5ba6a3aba4aba

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)
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