#13115 ⟨a, b | bbb=aaa, aaba=b⟩

Up:Monoids with two generators and two relations
Prev:#13110 ⟨a, b | bbb=aaa, aaaa=a⟩
Next:#13118 ⟨a, b | bbb=aaa, abba=a⟩

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. b10 ⇒ b
  2. ba ⇒ ab7
  3. a3 ⇒ b3 
# ab:bbb=aaa,aaba=b b/a
bbbbbbbbbb=b
ba=abbbbbbb
aaa=bbb

Right Cayley graph

Left Cayley graph

Others with same cardinality

8 unique, 123 total

Σ#PresentationDescriptionRelated
91470⟨a, b | aaa=bb, abab=1⟩Finite non-Abelian group with 30 elements73 iso
91907⟨a, b | aab=a, bbbbb=1⟩Finite non-commutative monoid with 30 elements11 iso, 4 anti-iso
92443⟨a, b | aaa=1, abbbb=b⟩Finite non-commutative monoid with 30 elements14 iso, 5 anti-iso
106560⟨a, b | aaa=a, bbbb=ab⟩Finite non-commutative monoid with 30 elements
107013⟨a, b | ab=aa, bbbbb=b⟩Finite non-commutative monoid with 30 elements
1111058⟨a, b | abba=bbb, baba=1⟩Finite non-Abelian group with 30 elements8 iso
1115979⟨a, b | aaa=aa, bbbb=ab⟩Finite non-commutative monoid with 30 elements
1120847⟨a, b | ab=aa, bbbbb=bb⟩Finite non-commutative monoid with 30 elements