#924 ⟨a, b | aaabbba=bb⟩

Up:Monoids with two generators and one relation
Prev:#923 ⟨a, b | aaabbba=ba⟩
Next:#925 ⟨a, b | aabaaab=aa⟩

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. a3b3a ⇒ b2 [1]
2. a3b5 ⇒ b2a2b3a [2]
# ab:aaabbba=bb ba
aaabbba=bb
aaabbbbb=bbaabbba

Other submonoids of same group

2 unique, 2 total

Σ#PresentationDescriptionRelated
91056⟨a, b | aaabba=bbb⟩Infinite cancellative non-commutative monoid
114305⟨a, b | abababbba=bb⟩Infinite cancellative non-commutative monoid

Other submonoids of anti-isomorphic group

1 unique, 1 total

Σ#PresentationDescriptionRelated
113777⟨a, b | abababbbba=b⟩Infinite cancellative non-commutative monoid