#5309 ⟨a, b | aaa=aa, 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 ⇒ b5
  2. ab ⇒ b3
  3. a3 ⇒ a2 
# ab:aaa=aa,bbb=ab b/a
bbbbbbb=bbbbb
ab=bbb
aaa=aa

Cayley table

Idempotents are shown in bold.

1aba2bab2ba2b2ab3b2a2b3ab4b3a2b4ab5b4a2b5ab6b5a2b6ab6a2
11aba2bab2ba2b2ab3b2a2b3ab4b3a2b4ab5b4a2b5ab6b5a2b6ab6a2
aaa2b3a2b3ab4b3a2b4ab5b4a2b5ab6b5a2b6ab5b6a2b5ab6b5a2b6ab6a2
bbbab2ba2b2ab3b2a2b3ab4b3a2b4ab5b4a2b5ab6b5a2b6ab5b6a2b5ab5a2
a2a2a2b5a2b5ab6b5a2b6ab5b6a2b5ab6b5a2b6ab5b6a2b5ab6b5a2b6ab6a2
bababa2b4ba2b4ab5b4a2b5ab6b5a2b6ab5b6a2b5ab6b5a2b6ab5b6a2b5ab5a2
b2b2b2ab3b2a2b3ab4b3a2b4ab5b4a2b5ab6b5a2b6ab5b6a2b5ab6b5a2b6ab6a2
ba2ba2ba2b6ba2b6ab5b6a2b5ab6b5a2b6ab5b6a2b5ab6b5a2b6ab5b6a2b5ab5a2
b2ab2ab2a2b5b2a2b5ab6b5a2b6ab5b6a2b5ab6b5a2b6ab5b6a2b5ab6b5a2b6ab6a2
b3b3b3ab4b3a2b4ab5b4a2b5ab6b5a2b6ab5b6a2b5ab6b5a2b6ab5b6a2b5ab5a2
b2a2b2a2b2a2b5b2a2b5ab6b5a2b6ab5b6a2b5ab6b5a2b6ab5b6a2b5ab6b5a2b6ab6a2
b3ab3ab3a2b6b3a2b6ab5b6a2b5ab6b5a2b6ab5b6a2b5ab6b5a2b6ab5b6a2b5ab5a2
b4b4b4ab5b4a2b5ab6b5a2b6ab5b6a2b5ab6b5a2b6ab5b6a2b5ab6b5a2b6ab6a2
b3a2b3a2b3a2b6b3a2b6ab5b6a2b5ab6b5a2b6ab5b6a2b5ab6b5a2b6ab5b6a2b5ab5a2
b4ab4ab4a2b5b4a2b5ab6b5a2b6ab5b6a2b5ab6b5a2b6ab5b6a2b5ab6b5a2b6ab6a2
b5b5b5ab6b5a2b6ab5b6a2b5ab6b5a2b6ab5b6a2b5ab6b5a2b6ab5b6a2b5ab5a2
b4a2b4a2b4a2b5b4a2b5ab6b5a2b6ab5b6a2b5ab6b5a2b6ab5b6a2b5ab6b5a2b6ab6a2
b5ab5ab5a2b6b5a2b6ab5b6a2b5ab6b5a2b6ab5b6a2b5ab6b5a2b6ab5b6a2b5ab5a2
b6b6b6ab5b6a2b5ab6b5a2b6ab5b6a2b5ab6b5a2b6ab5b6a2b5ab6b5a2b6ab6a2
b5a2b5a2b5a2b6b5a2b6ab5b6a2b5ab6b5a2b6ab5b6a2b5ab6b5a2b6ab5b6a2b5ab5a2
b6ab6ab6a2b5b6a2b5ab6b5a2b6ab5b6a2b5ab6b5a2b6ab5b6a2b5ab6b5a2b6ab6a2
b6a2b6a2b6a2b5b6a2b5ab6b5a2b6ab5b6a2b5ab6b5a2b6ab5b6a2b5ab6b5a2b6ab6a2

Right Cayley graph

Idempotents are shown in bold.

Left Cayley graph

Idempotents are shown in bold.

Others with same cardinality

8 unique, 64 total

Σ#PresentationDescriptionRelated
8402⟨a, b | aaa=ab, bbb=1⟩Finite non-commutative monoid with 21 elements12 iso, 27 anti-iso
91599⟨a, b | aaa=ab, bbb=b⟩Finite non-commutative monoid with 21 elements1 anti-iso
106265⟨a, b | aaa=a, abbbb=b⟩Finite non-commutative monoid with 21 elements2 iso
1111127⟨a, b | aaaaa=b, abbbb=1⟩Isomorphic to ℤ2113 iso
1113091⟨a, b | bab=aaa, abba=b⟩Finite non-commutative monoid with 21 elements
1113248⟨a, b | bab=aaa, bbb=aa⟩Finite non-commutative monoid with 21 elements
1115158⟨a, b | aab=ba, ababab=1⟩Finite non-Abelian group with 21 elements1 iso
1119212⟨a, b | aba=b, baaaab=a⟩Finite non-commutative monoid with 21 elements