#5771 ⟨a, b | aabbab=bbaba⟩

Up:Monoids with two generators and one relation
Prev:#5770 ⟨a, b | aabbab=bbaab⟩
Next:#5772 ⟨a, b | aabbab=bbabb⟩

Quick links

  1. Properties
  2. Rewriting system
  3. Other submonoids of same group
  4. Other submonoids of anti-isomorphic 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. a2b2ab ⇒ b(ba)2 [1]
# ab:aabbab=bbaba ab
aabbab=bbaba

Other submonoids of same group

2 unique, 2 total

Σ#PresentationDescriptionRelated
115159⟨a, b | aabaabb=baba⟩Infinite cancellative non-commutative monoid
115722⟨a, b | aababb=baaba⟩Infinite cancellative non-commutative monoid

Other submonoids of anti-isomorphic group

1 unique, 1 total

Σ#PresentationDescriptionRelated
115319⟨a, b | abaabab=bbaa⟩Infinite cancellative non-commutative monoid