#222 ⟨a, b | aabba=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. a2b2a ⇒ b2 [1]
2. a2b4 ⇒ (b2a)2 [2]
# ab:aabba=bb ba
aabba=bb
aabbbb=bbabba

Other submonoids of same group

5 unique, 10 total

Σ#PresentationDescriptionRelated
8406⟨a, b | ababbba=b⟩Infinite cancellative non-commutative monoid
9631⟨a, b | aaabaabba=1⟩Infinite non-Abelian group5 iso
91074⟨a, b | aababa=bab⟩Infinite cancellative non-commutative monoid
113737⟨a, b | abaabababa=b⟩Infinite cancellative non-commutative monoid
115142⟨a, b | aabaaba=baab⟩Infinite cancellative non-commutative monoid