#110 ⟨a, b | abab=ba⟩

Up:Monoids with two generators and one relation
Prev:#109 ⟨a, b | abab=ab⟩
Next:#111 ⟨a, b | abba=aa⟩

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. c2b ⇒ bc [5]
2. acb ⇒ c [4]
3. ba ⇒ c [2]
4. ca ⇒ ac2 [6]
# ab:abab=ba bc/a ba=c magic:0
ccb=bc
acb=c
ba=c
ca=acc

Other submonoids of same group

9 unique, 9 total

Σ#PresentationDescriptionRelated
549⟨a, b | aab=ba⟩Infinite cancellative non-commutative monoid
7225⟨a, b | abaab=ba⟩Infinite cancellative non-commutative monoid
8467⟨a, b | abaaab=ba⟩Infinite cancellative non-commutative monoid
9969⟨a, b | abaaaab=ba⟩Infinite cancellative non-commutative monoid
9984⟨a, b | ababaab=ba⟩Infinite cancellative non-commutative monoid
102021⟨a, b | abaaaaab=ba⟩Infinite cancellative non-commutative monoid
114227⟨a, b | abaaaaaab=ba⟩Infinite cancellative non-commutative monoid
114258⟨a, b | abaabaaab=ba⟩Infinite cancellative non-commutative monoid
114297⟨a, b | abababaab=ba⟩Infinite cancellative non-commutative monoid