#124 ⟨a, b | bbb=aaa⟩

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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. b3 ⇒ a3 [1]
2. ba3 ⇒ a3b [2]
# ab:bbb=aaa ab
bbb=aaa
baaa=aaab

Other submonoids of same group

5 unique, 14 total

Σ#PresentationDescriptionRelated
667⟨a, b | aabbba=1⟩Infinite non-Abelian group8 iso
7229⟨a, b | ababa=bb⟩Infinite cancellative non-commutative monoid
8410⟨a, b | abbabba=b⟩Infinite cancellative non-commutative monoid1 iso
91115⟨a, b | abaaba=bab⟩Infinite cancellative non-commutative monoid
115304⟨a, b | abaaaba=baab⟩Infinite cancellative non-commutative monoid