#1221 ⟨a, b | aabab=bbba⟩

Up:Monoids with two generators and one relation
Prev:#1220 ⟨a, b | aabab=bbab⟩
Next:#1222 ⟨a, b | aabab=bbbb⟩

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(ab)2 ⇒ b3a [1]
# ab:aabab=bbba ab
aabab=bbba

Other submonoids of same group

2 unique, 2 total

Σ#PresentationDescriptionRelated
9911⟨a, b | aaababb=ba⟩Infinite cancellative non-commutative monoid
113973⟨a, b | aaabaabab=ba⟩Infinite cancellative non-commutative monoid

Other submonoids of anti-isomorphic group

2 unique, 2 total

Σ#PresentationDescriptionRelated
102243⟨a, b | aababab=bba⟩Infinite cancellative non-commutative monoid
115315⟨a, b | abaabab=baaa⟩Infinite cancellative non-commutative monoid