#2487 ⟨a, b | aabaab=baaa⟩

Up:Monoids with two generators and one relation
Prev:#2486 ⟨a, b | aabaab=abbb⟩
Next:#2488 ⟨a, b | aabaab=baab⟩

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. ca3 ⇒ a2c2 [4]
2. ba3 ⇒ c2 [3]
3. a2b ⇒ c [2]
4. c2b ⇒ bac [5]
5. c2ab ⇒ ba2c [6]
# ab:aabaab=baaa ac/b aab=c morph:3/0
caaa=aacc
baaa=cc
aab=c
ccb=bac
ccab=baac

Other submonoids of same group

6 unique, 6 total

Σ#PresentationDescriptionRelated
8511⟨a, b | aaabb=baa⟩Infinite cancellative non-commutative monoid
8582⟨a, b | baaa=aabb⟩Infinite cancellative non-commutative monoid
91045⟨a, b | aaabab=baa⟩Infinite cancellative non-commutative monoid
102163⟨a, b | aaabaab=baa⟩Infinite cancellative non-commutative monoid
114487⟨a, b | aaabaaab=baa⟩Infinite cancellative non-commutative monoid
115875⟨a, b | ababab=babaa⟩Infinite cancellative non-commutative monoid

Other submonoids of anti-isomorphic group

3 unique, 3 total

Σ#PresentationDescriptionRelated
91215⟨a, b | aabab=baaa⟩Infinite cancellative non-commutative monoid
115125⟨a, b | aabaaab=baaa⟩Infinite cancellative non-commutative monoid
115185⟨a, b | aababab=baba⟩Infinite cancellative non-commutative monoid