#254 ⟨a, b | aaba=bbb⟩

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  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. a2ba ⇒ b3 [1]
2. b3aba ⇒ a2b4 [2]
# ab:aaba=bbb ab
aaba=bbb
bbbaba=aabbbb

Other submonoids of same group

6 unique, 25 total

Σ#PresentationDescriptionRelated
8290⟨a, b | aaababba=1⟩Infinite non-Abelian group9 iso, 10 anti-iso
8478⟨a, b | ababba=bb⟩Infinite cancellative non-commutative monoid
9863⟨a, b | abbabbba=b⟩Infinite cancellative non-commutative monoid
91263⟨a, b | ababa=babb⟩Infinite cancellative non-commutative monoid
114796⟨a, b | abaababa=bab⟩Infinite cancellative non-commutative monoid
115405⟨a, b | abbabba=babb⟩Infinite cancellative non-commutative monoid

Other submonoids of anti-isomorphic group

3 unique, 3 total

Σ#PresentationDescriptionRelated
7186⟨a, b | aabbba=b⟩Infinite cancellative non-commutative monoid
9804⟨a, b | aabababa=b⟩Infinite cancellative non-commutative monoid
113560⟨a, b | aabaabaaba=b⟩Infinite cancellative non-commutative monoid