#1008 ⟨a, b | aaaaaa=bbb⟩

Up:Monoids with two generators and one relation
Prev:#1007 ⟨a, b | aaaaaa=bab⟩
Next:#1009 ⟨a, b | aaaaab=aaa⟩

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. a6 ⇒ b3 [1]
# ab:aaaaaa=bbb ab
bbba=abbb
aaaaaa=bbb

Other submonoids of same group

3 unique, 6 total

Σ#PresentationDescriptionRelated
9609⟨a, b | aaaaabbba=1⟩Infinite non-Abelian group3 iso
102764⟨a, b | babab=aaaaa⟩Infinite cancellative non-commutative monoid
115406⟨a, b | abbabba=bbbb⟩Infinite cancellative non-commutative monoid