#1180 ⟨a, b | aaaba=bbbb⟩

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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. a3ba ⇒ b4 [1]
2. b4a2ba ⇒ a3b5 [2]
# ab:aaaba=bbbb ab
aaaba=bbbb
bbbbaaba=aaabbbbb

Other submonoids of same group

2 unique, 8 total

Σ#PresentationDescriptionRelated
112861⟨a, b | aaaabababba=1⟩Infinite non-Abelian group2 iso, 4 anti-iso
114830⟨a, b | abababba=bbb⟩Infinite cancellative non-commutative monoid

Other submonoids of anti-isomorphic group

1 unique, 1 total

Σ#PresentationDescriptionRelated
9788⟨a, b | aaabbbba=b⟩Infinite cancellative non-commutative monoid