#2765 ⟨a, b | babab=aaaba⟩

Up:Monoids with two generators and one relation
Prev:#2764 ⟨a, b | babab=aaaaa⟩
Next:#2766 ⟨a, b | babab=aabaa⟩

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(a2b)2 ⇒ ba4ba [2]
2. b(ab)2 ⇒ a3ba [1]
# ab:babab=aaaba a/b
aaabaab=baaaaba
babab=aaaba

Other submonoids of same group

3 unique, 8 total

Σ#PresentationDescriptionRelated
8506⟨a, b | aaaba=bbb⟩Infinite cancellative non-commutative monoid
101356⟨a, b | aaabababba=1⟩Infinite non-Abelian group2 iso, 3 anti-iso
102059⟨a, b | abababba=bb⟩Infinite cancellative non-commutative monoid

Other submonoids of anti-isomorphic group

2 unique, 2 total

Σ#PresentationDescriptionRelated
8370⟨a, b | aaabbba=b⟩Infinite cancellative non-commutative monoid
101628⟨a, b | aaabababa=b⟩Infinite cancellative non-commutative monoid