#5856 ⟨a, b | abaaba=baabb⟩

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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. ba2b2 ⇒ (aba)2 [1]
2. aba2ba3b2 ⇒ (ba2ba)2 [2]
# ab:abaaba=baabb a/b
baabb=abaaba
abaabaaabb=baababaaba

Other submonoids of same group

3 unique, 9 total

Σ#PresentationDescriptionRelated
9981⟨a, b | abaabba=bb⟩Infinite cancellative non-commutative monoid
112932⟨a, b | aaababaabba=1⟩Infinite non-Abelian group2 iso, 4 anti-iso
113816⟨a, b | abbababbba=b⟩Infinite cancellative non-commutative monoid

Other submonoids of anti-isomorphic group

2 unique, 2 total

Σ#PresentationDescriptionRelated
9845⟨a, b | abaabbba=b⟩Infinite cancellative non-commutative monoid
114712⟨a, b | aabbabba=bab⟩Infinite cancellative non-commutative monoid