#947 ⟨a, b | aababba=bb⟩

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Quick links

  1. Properties
  2. Rewriting system
  3. Other submonoids of same group
  4. Other submonoids of anti-isomorphic 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. a2bab2a ⇒ b2 [1]
2. a2bab4 ⇒ b(ba)2b2a [2]
# ab:aababba=bb ba
aababba=bb
aababbbb=bbababba

Other submonoids of same group

2 unique, 8 total

Σ#PresentationDescriptionRelated
112918⟨a, b | aaabaababba=1⟩Infinite non-Abelian group3 iso, 3 anti-iso
113786⟨a, b | ababbabbba=b⟩Infinite cancellative non-commutative monoid

Other submonoids of anti-isomorphic group

2 unique, 2 total

Σ#PresentationDescriptionRelated
9811⟨a, b | aababbba=b⟩Infinite cancellative non-commutative monoid
102508⟨a, b | aababa=bbab⟩Infinite cancellative non-commutative monoid