#973 ⟨a, b | abaaaba=bb⟩

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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. b2a2ba ⇒ aba2b2 [2]
2. aba3ba ⇒ b2 [1]
3. b3a3ba ⇒ aba3b3 [3]
# ab:abaaaba=bb ab
bbaaba=abaabb
abaaaba=bb
bbbaaaba=abaaabbb

Other submonoids of same group

2 unique, 6 total

Σ#PresentationDescriptionRelated
101451⟨a, b | aabbababba=1⟩Infinite non-Abelian group4 iso
114765⟨a, b | abaaaaba=bab⟩Infinite cancellative non-commutative monoid