#386 ⟨a, b | aabbaba=b⟩

Up:Monoids with two generators and one relation
Prev:#385 ⟨a, b | aabbaba=a⟩
Next:#387 ⟨a, b | aabbbaa=a⟩

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. a(ab2)2 ⇒ (bab)2a [2]
2. a2b(ba)2 ⇒ b [1]
# ab:aabbaba=b ba
aabbabb=babbaba
aabbaba=b

Other submonoids of same group

3 unique, 8 total

Σ#PresentationDescriptionRelated
8591⟨a, b | babb=aaba⟩Infinite cancellative non-commutative monoid
101410⟨a, b | aabaabbaba=1⟩Infinite non-Abelian group2 iso, 3 anti-iso
101690⟨a, b | aababaaba=b⟩Infinite cancellative non-commutative monoid

Other submonoids of anti-isomorphic group

1 unique, 1 total

Σ#PresentationDescriptionRelated
102610⟨a, b | ababba=babb⟩Infinite cancellative non-commutative monoid