#426 ⟨a, b | aaaabb=ba⟩

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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. a4b2 ⇒ ba [1]
# ab:aaaabb=ba ab
aaaabb=ba

Other submonoids of same group

5 unique, 5 total

Σ#PresentationDescriptionRelated
9888⟨a, b | aaaabab=ba⟩Infinite cancellative non-commutative monoid
101856⟨a, b | aaaabaab=ba⟩Infinite cancellative non-commutative monoid
102737⟨a, b | baaaa=abaab⟩Infinite cancellative non-commutative monoid
113901⟨a, b | aaaabaaab=ba⟩Infinite cancellative non-commutative monoid
114822⟨a, b | abababab=baa⟩Infinite cancellative non-commutative monoid

Other submonoids of anti-isomorphic group

4 unique, 4 total

Σ#PresentationDescriptionRelated
8497⟨a, b | aaaab=bba⟩Infinite cancellative non-commutative monoid
91159⟨a, b | aaaab=baba⟩Infinite cancellative non-commutative monoid
114125⟨a, b | aabababab=ba⟩Infinite cancellative non-commutative monoid
115825⟨a, b | abaaab=baaaa⟩Infinite cancellative non-commutative monoid