#2508 ⟨a, b | aababa=bbab⟩

Up:Monoids with two generators and one relation
Prev:#2507 ⟨a, b | aababa=bbaa⟩
Next:#2509 ⟨a, b | aababa=bbba⟩

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. b2ab ⇒ a2(ba)2 [1]
2. a(ab)4 ⇒ b2a3(ba)2 [2]
# ab:aababa=bbab a/b
bbab=aababa
aabababab=bbaaababa

Other submonoids of same group

3 unique, 9 total

Σ#PresentationDescriptionRelated
9947⟨a, b | aababba=bb⟩Infinite cancellative non-commutative monoid
112918⟨a, b | aaabaababba=1⟩Infinite non-Abelian group3 iso, 3 anti-iso
113786⟨a, b | ababbabbba=b⟩Infinite cancellative non-commutative monoid

Other submonoids of anti-isomorphic group

1 unique, 1 total

Σ#PresentationDescriptionRelated
9811⟨a, b | aababbba=b⟩Infinite cancellative non-commutative monoid