#238 ⟨a, b | aaaa=bbb⟩

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Quick links

  1. Properties
  2. Rewriting system
  3. Other submonoids of same 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. a4 ⇒ b3 [1]
2. b3a ⇒ ab3 [2]
# ab:aaaa=bbb ab
aaaa=bbb
bbba=abbb

Other submonoids of same group

7 unique, 23 total

Σ#PresentationDescriptionRelated
7139⟨a, b | aaabbba=1⟩Infinite non-Abelian group16 iso
8550⟨a, b | ababa=bbb⟩Infinite cancellative non-commutative monoid
9988⟨a, b | abababa=bb⟩Infinite cancellative non-commutative monoid
9999⟨a, b | abbabba=bb⟩Infinite cancellative non-commutative monoid
101816⟨a, b | abbbabbba=b⟩Infinite cancellative non-commutative monoid
113820⟨a, b | abbabbabba=b⟩Infinite cancellative non-commutative monoid
115857⟨a, b | abaaba=babab⟩Infinite cancellative non-commutative monoid