#1045 ⟨a, b | aaabab=baa⟩

Up:Monoids with two generators and one relation
Prev:#1044 ⟨a, b | aaabab=abb⟩
Next:#1046 ⟨a, b | aaabab=bab⟩

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. a3bab ⇒ ba2 [1]
# ab:aaabab=baa ab
aaabab=baa

Other submonoids of same group

5 unique, 5 total

Σ#PresentationDescriptionRelated
8511⟨a, b | aaabb=baa⟩Infinite cancellative non-commutative monoid
8582⟨a, b | baaa=aabb⟩Infinite cancellative non-commutative monoid
102163⟨a, b | aaabaab=baa⟩Infinite cancellative non-commutative monoid
114487⟨a, b | aaabaaab=baa⟩Infinite cancellative non-commutative monoid
115875⟨a, b | ababab=babaa⟩Infinite cancellative non-commutative monoid

Other submonoids of anti-isomorphic group

4 unique, 4 total

Σ#PresentationDescriptionRelated
91215⟨a, b | aabab=baaa⟩Infinite cancellative non-commutative monoid
102487⟨a, b | aabaab=baaa⟩Infinite cancellative non-commutative monoid
115125⟨a, b | aabaaab=baaa⟩Infinite cancellative non-commutative monoid
115185⟨a, b | aababab=baba⟩Infinite cancellative non-commutative monoid