#955 ⟨a, b | aabbaba=bb⟩

Up:Monoids with two generators and one relation
Prev:#954 ⟨a, b | aabbaba=ba⟩
Next:#956 ⟨a, b | aabbbaa=aa⟩

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. a2b(ba)2 ⇒ b2 [1]
2. (b2a)2ba ⇒ a2b2ab3 [2]
# ab:aabbaba=bb ab
aabbaba=bb
bbabbaba=aabbabbb

Other submonoids of same group

3 unique, 9 total

Σ#PresentationDescriptionRelated
9824⟨a, b | aabbbaba=b⟩Infinite cancellative non-commutative monoid
112922⟨a, b | aaabaabbaba=1⟩Infinite non-Abelian group3 iso, 3 anti-iso
113790⟨a, b | ababbbabba=b⟩Infinite cancellative non-commutative monoid

Other submonoids of anti-isomorphic group

1 unique, 1 total

Σ#PresentationDescriptionRelated
102506⟨a, b | aababa=babb⟩Infinite cancellative non-commutative monoid