#2766 ⟨a, b | babab=aabaa⟩

Up:Monoids with two generators and one relation
Prev:#2765 ⟨a, b | babab=aaaba⟩
Next:#2767 ⟨a, b | babab=ababa⟩

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. a2ba2 ⇒ b(ab)2 [1]
2. a2b2(ab)2 ⇒ (ba)2b2a2 [2]
3. a(ab)4 ⇒ (ba)4a [3]
# ab:babab=aabaa ba
aabaa=babab
aabbabab=bababbaa
aabababab=babababaa

Other submonoids of same group

5 unique, 8 total

Σ#PresentationDescriptionRelated
8388⟨a, b | aabbbaa=b⟩Infinite cancellative non-commutative monoid
8520⟨a, b | aabaa=bbb⟩Infinite cancellative non-commutative monoid
101360⟨a, b | aaababbaba=1⟩Infinite non-Abelian group3 iso
101694⟨a, b | aabababaa=b⟩Infinite cancellative non-commutative monoid
102066⟨a, b | ababbaba=bb⟩Infinite cancellative non-commutative monoid