#471 ⟨a, b | abaaba=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. b(ba)2 ⇒ abab2 [2]
2. (aba)2 ⇒ b2 [1]
3. b3a2ba ⇒ aba2b3 [3]
# ab:abaaba=bb ab
bbaba=ababb
abaaba=bb
bbbaaba=abaabbb

Other submonoids of same group

3 unique, 5 total

Σ#PresentationDescriptionRelated
8315⟨a, b | aabbabba=1⟩Infinite non-Abelian group2 iso
101810⟨a, b | abbababba=b⟩Infinite cancellative non-commutative monoid
102303⟨a, b | abaaaba=bab⟩Infinite cancellative non-commutative monoid