#506 ⟨a, b | aaaba=bbb⟩

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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. a3ba ⇒ b3 [1]
2. b3a2ba ⇒ a3b4 [2]
# ab:aaaba=bbb ab
aaaba=bbb
bbbaaba=aaabbbb

Other submonoids of same group

2 unique, 7 total

Σ#PresentationDescriptionRelated
101356⟨a, b | aaabababba=1⟩Infinite non-Abelian group2 iso, 3 anti-iso
102059⟨a, b | abababba=bb⟩Infinite cancellative non-commutative monoid

Other submonoids of anti-isomorphic group

3 unique, 3 total

Σ#PresentationDescriptionRelated
8370⟨a, b | aaabbba=b⟩Infinite cancellative non-commutative monoid
101628⟨a, b | aaabababa=b⟩Infinite cancellative non-commutative monoid
102765⟨a, b | babab=aaaba⟩Infinite cancellative non-commutative monoid