#23 ⟨a, b | bb=aa⟩

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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. b2 ⇒ a2 [1]
2. ba2 ⇒ a2b [2]
# ab:bb=aa ab
bb=aa
baa=aab

Other submonoids of same group

2 unique, 16 total

Σ#PresentationDescriptionRelated
414⟨a, b | abba=1⟩Infinite non-Abelian group14 iso
420⟨a, b | aba=b⟩Infinite cancellative non-commutative monoid