#1690 ⟨a, b | aababaaba=b⟩

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  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. a2bab2 ⇒ b2a2ba [2]
2. a(ab)2a2b2 ⇒ (ba)3aba [3]
3. a2b(aba)2 ⇒ b [1]
# ab:aababaaba=b ba
aababb=bbaaba
aababaabb=bababaaba
aababaaba=b

Other submonoids of same group

3 unique, 8 total

Σ#PresentationDescriptionRelated
8386⟨a, b | aabbaba=b⟩Infinite cancellative non-commutative monoid
8591⟨a, b | babb=aaba⟩Infinite cancellative non-commutative monoid
101410⟨a, b | aabaabbaba=1⟩Infinite non-Abelian group2 iso, 3 anti-iso

Other submonoids of anti-isomorphic group

1 unique, 1 total

Σ#PresentationDescriptionRelated
102610⟨a, b | ababba=babb⟩Infinite cancellative non-commutative monoid