#2764 ⟨a, b | babab=aaaaa⟩

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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(ab)2 ⇒ a5 [1]
2. ba6 ⇒ a6b [2]
# ab:babab=aaaaa ab
babab=aaaaa
baaaaaa=aaaaaab

Other submonoids of same group

3 unique, 6 total

Σ#PresentationDescriptionRelated
9609⟨a, b | aaaaabbba=1⟩Infinite non-Abelian group3 iso
91008⟨a, b | aaaaaa=bbb⟩Infinite cancellative non-commutative monoid
115406⟨a, b | abbabba=bbbb⟩Infinite cancellative non-commutative monoid