#229 ⟨a, b | ababa=bb⟩

Up:Monoids with two generators and one relation
Prev:#228 ⟨a, b | ababa=ab⟩
Next:#230 ⟨a, b | abbba=aa⟩

Quick links

  1. Properties
  2. Rewriting system
  3. Other submonoids of same group

Properties

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
#RuleProof
1. b3a ⇒ ab3 [2]
2. a(ba)2 ⇒ b2 [1]
# ab:ababa=bb ab
bbba=abbb
ababa=bb

Other submonoids of same group

5 unique, 14 total

Σ#PresentationDescriptionRelated
667⟨a, b | aabbba=1⟩Infinite non-Abelian group8 iso
6124⟨a, b | bbb=aaa⟩Infinite cancellative non-commutative monoid
8410⟨a, b | abbabba=b⟩Infinite cancellative non-commutative monoid1 iso
91115⟨a, b | abaaba=bab⟩Infinite cancellative non-commutative monoid
115304⟨a, b | abaaaba=baab⟩Infinite cancellative non-commutative monoid