#13142 ⟨a, b | aab=aaa, bbb=ba⟩

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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. ba ⇒ b3
  3. a2b3 ⇒ a2b2
  4. a3 ⇒ a2b 
# ab:aab=aaa,bbb=ba b/a
bbbbbbb=bbbbbb
ba=bbb
aabbb=aabb
aaa=aab

Cayley table

Idempotents are shown in bold.

1aba2abb2a2bab2b3a2b2ab3b4ab4b5ab5b6ab6
11aba2abb2a2bab2b3a2b2ab3b4ab4b5ab5b6ab6
aaa2aba2ba2bab2a2b2a2b2ab3a2b2a2b2ab4a2b2ab5a2b2ab6a2b2
bbb3b2b5b4b3b6b5b4b6b6b5b6b6b6b6b6
a2a2a2ba2ba2b2a2b2a2b2a2b2a2b2a2b2a2b2a2b2a2b2a2b2a2b2a2b2a2b2a2b2
ababab3ab2ab5ab4ab3ab6ab5ab4ab6ab6ab5ab6ab6ab6ab6ab6
b2b2b4b3b6b5b4b6b6b5b6b6b6b6b6b6b6b6
a2ba2ba2b2a2b2a2b2a2b2a2b2a2b2a2b2a2b2a2b2a2b2a2b2a2b2a2b2a2b2a2b2a2b2
ab2ab2ab4ab3ab6ab5ab4ab6ab6ab5ab6ab6ab6ab6ab6ab6ab6ab6
b3b3b5b4b6b6b5b6b6b6b6b6b6b6b6b6b6b6
a2b2a2b2a2b2a2b2a2b2a2b2a2b2a2b2a2b2a2b2a2b2a2b2a2b2a2b2a2b2a2b2a2b2a2b2
ab3ab3ab5ab4ab6ab6ab5ab6ab6ab6ab6ab6ab6ab6ab6ab6ab6ab6
b4b4b6b5b6b6b6b6b6b6b6b6b6b6b6b6b6b6
ab4ab4ab6ab5ab6ab6ab6ab6ab6ab6ab6ab6ab6ab6ab6ab6ab6ab6
b5b5b6b6b6b6b6b6b6b6b6b6b6b6b6b6b6b6
ab5ab5ab6ab6ab6ab6ab6ab6ab6ab6ab6ab6ab6ab6ab6ab6ab6ab6
b6b6b6b6b6b6b6b6b6b6b6b6b6b6b6b6b6b6
ab6ab6ab6ab6ab6ab6ab6ab6ab6ab6ab6ab6ab6ab6ab6ab6ab6ab6

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