#13156 ⟨a, b | aba=aaa, bbb=ab⟩

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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. b7 ⇒ b6
  2. ab ⇒ b3
  3. b3a2 ⇒ b5a
  4. a3 ⇒ b3a 
# ab:aba=aaa,bbb=ab b/a
bbbbbbb=bbbbbb
ab=bbb
bbbaa=bbbbba
aaa=bbba

Cayley table

Idempotents are shown in bold.

1aba2bab2ba2b2ab3b2a2b3ab4b4ab5b5ab6b6a
11aba2bab2ba2b2ab3b2a2b3ab4b4ab5b5ab6b6a
aaa2b3b3ab3ab4b5ab4ab5b6ab5ab6b6ab6b6ab6b6a
bbbab2ba2b2ab3b2a2b3ab4b5ab4ab5b5ab6b6ab6b6a
a2a2b3ab5b5ab5ab6b6ab6ab6b6ab6ab6b6ab6b6ab6b6a
bababa2b4b4ab4ab5b6ab5ab6b6ab6ab6b6ab6b6ab6b6a
b2b2b2ab3b2a2b3ab4b5ab4ab5b6ab5ab6b6ab6b6ab6b6a
ba2ba2b4ab6b6ab6ab6b6ab6ab6b6ab6ab6b6ab6b6ab6b6a
b2ab2ab2a2b5b5ab5ab6b6ab6ab6b6ab6ab6b6ab6b6ab6b6a
b3b3b3ab4b5ab4ab5b6ab5ab6b6ab6ab6b6ab6b6ab6b6a
b2a2b2a2b5ab6b6ab6ab6b6ab6ab6b6ab6ab6b6ab6b6ab6b6a
b3ab3ab5ab6b6ab6ab6b6ab6ab6b6ab6ab6b6ab6b6ab6b6a
b4b4b4ab5b6ab5ab6b6ab6ab6b6ab6ab6b6ab6b6ab6b6a
b4ab4ab6ab6b6ab6ab6b6ab6ab6b6ab6ab6b6ab6b6ab6b6a
b5b5b5ab6b6ab6ab6b6ab6ab6b6ab6ab6b6ab6b6ab6b6a
b5ab5ab6ab6b6ab6ab6b6ab6ab6b6ab6ab6b6ab6b6ab6b6a
b6b6b6ab6b6ab6ab6b6ab6ab6b6ab6ab6b6ab6b6ab6b6a
b6ab6ab6ab6b6ab6ab6b6ab6ab6b6ab6ab6b6ab6b6ab6b6a

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
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
1116521⟨a, b | aab=bb, bab=aaa⟩Finite non-commutative monoid with 17 elements