#16521 ⟨a, b | aab=bb, bab=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. a8 ⇒ a6
  2. ba3 ⇒ a5
  3. a3b ⇒ a7
  4. b2 ⇒ a2b
  5. bab ⇒ a3
  6. ba2b ⇒ a6 
# ab:aab=bb,bab=aaa a/b
aaaaaaaa=aaaaaa
baaa=aaaaa
aaab=aaaaaaa
bb=aab
bab=aaa
baab=aaaaaa

Cayley table

Idempotents are shown in bold.

1aba2abbaa3a2bababa2a4a2baaba2a5a2ba2a6a7
11aba2abbaa3a2bababa2a4a2baaba2a5a2ba2a6a7
aaa2aba3a2babaa4a7a2baaba2a5a6a2ba2a6a7a7a6
bbbaa2bba2a3a2baa5a6a4a2ba2a6a7a5a7a6a6a7
a2a2a3a2ba4a7a2baa5a6a6a2ba2a6a7a7a7a6a6a7
abababaa7aba2a4a6a6a7a5a7a7a6a6a6a7a7a6
bababa2a3a5a6a4a6a7a7a5a7a6a6a6a7a7a6
a3a3a4a7a5a6a6a6a7a7a7a7a6a6a6a7a7a6
a2ba2ba2baa6a2ba2a5a7a7a6a6a6a6a7a7a7a6a6a7
abaabaaba2a4a6a7a5a7a6a6a6a6a7a7a7a6a6a7
ba2ba2a5a6a6a7a7a7a6a6a6a6a7a7a7a6a6a7
a4a4a5a6a6a7a7a7a6a6a6a6a7a7a7a6a6a7
a2baa2baa2ba2a5a7a6a6a6a7a7a7a7a6a6a6a7a7a6
aba2aba2a6a7a7a6a6a6a7a7a7a7a6a6a6a7a7a6
a5a5a6a7a7a6a6a6a7a7a7a7a6a6a6a7a7a6
a2ba2a2ba2a7a6a6a7a7a7a6a6a6a6a7a7a7a6a6a7
a6a6a7a6a6a7a7a7a6a6a6a6a7a7a7a6a6a7
a7a7a6a7a7a6a6a6a7a7a7a7a6a6a6a7a7a6

Right Cayley graph

Idempotents are shown in bold.

Left Cayley graph

Idempotents are shown in bold.

Others with same cardinality

16 unique, 71 total

Σ#PresentationDescriptionRelated
104375⟨a, b | aaaa=b, abbbb=1⟩Isomorphic to ℤ1739 iso
106428⟨a, b | aab=b, babbb=a⟩Finite non-commutative monoid with 17 elements2 iso
106514⟨a, b | aba=b, baaab=a⟩Finite non-commutative monoid with 17 elements
107152⟨a, b | bb=aa, abab=aa⟩Finite non-commutative monoid with 17 elements
107153⟨a, b | bb=aa, abab=ab⟩Finite non-commutative monoid with 17 elements
107154⟨a, b | bb=aa, abab=ba⟩Finite non-commutative monoid with 17 elements
1113141⟨a, b | aab=aaa, bbb=ab⟩Finite non-commutative monoid with 17 elements
1113142⟨a, b | aab=aaa, bbb=ba⟩Finite non-commutative monoid with 17 elements
1113151⟨a, b | aba=aaa, baa=bb⟩Finite non-commutative monoid with 17 elements
1113156⟨a, b | aba=aaa, bbb=ab⟩Finite non-commutative monoid with 17 elements
1113218⟨a, b | abb=aba, bbb=aa⟩Finite non-commutative monoid with 17 elements
1114395⟨a, b | aaaa=b, abbbb=a⟩Isomorphic to ℕ(17 = 1)2 iso
1114396⟨a, b | aaaa=b, abbbb=b⟩Isomorphic to ℕ(17 = 4)2 iso
1114698⟨a, b | aabb=a, baaaa=b⟩Finite non-commutative monoid with 17 elements1 iso, 6 anti-iso
1115488⟨a, b | aaa=ab, babbb=b⟩Finite non-commutative monoid with 17 elements3 iso
1116143⟨a, b | aab=aa, bbbb=ba⟩Finite non-commutative monoid with 17 elements