#5698 ⟨a, b | aababa=babab⟩

Up:Monoids with two generators and one relation
Prev:#5697 ⟨a, b | aababa=babaa⟩
Next:#5699 ⟨a, b | aababa=babba⟩

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. a2(ba)2 ⇒ b(ab)2 [1]
2. a2(bab)2ab ⇒ (ba)5 [2]
# ab:aababa=babab ba
aababa=babab
aababbabab=bababababa

Other submonoids of same group

4 unique, 18 total

Σ#PresentationDescriptionRelated
8536⟨a, b | aabba=bbb⟩Infinite cancellative non-commutative monoid
9992⟨a, b | ababbba=bb⟩Infinite cancellative non-commutative monoid
101312⟨a, b | aaaabaabba=1⟩Infinite non-Abelian group6 iso, 8 anti-iso
101812⟨a, b | abbabbbba=b⟩Infinite cancellative non-commutative monoid

Other submonoids of anti-isomorphic group

3 unique, 3 total

Σ#PresentationDescriptionRelated
8464⟨a, b | aabbba=bb⟩Infinite cancellative non-commutative monoid
9856⟨a, b | ababbbba=b⟩Infinite cancellative non-commutative monoid
114648⟨a, b | aabababa=bab⟩Infinite cancellative non-commutative monoid