#1128 ⟨a, b | ababba=bbb⟩

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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. abab2a ⇒ b3 [1]
2. b4ab2a ⇒ abab5 [2]
# ab:ababba=bbb ab
ababba=bbb
bbbbabba=ababbbbb

Other submonoids of same group

4 unique, 9 total

Σ#PresentationDescriptionRelated
9617⟨a, b | aaaababba=1⟩Infinite non-Abelian group2 iso, 3 anti-iso
102084⟨a, b | abbabbba=bb⟩Infinite cancellative non-commutative monoid
113829⟨a, b | abbbabbbba=b⟩Infinite cancellative non-commutative monoid
115363⟨a, b | abababa=babb⟩Infinite cancellative non-commutative monoid

Other submonoids of anti-isomorphic group

3 unique, 3 total

Σ#PresentationDescriptionRelated
8392⟨a, b | aabbbba=b⟩Infinite cancellative non-commutative monoid
8590⟨a, b | babb=aaaa⟩Infinite cancellative non-commutative monoid
113593⟨a, b | aababababa=b⟩Infinite cancellative non-commutative monoid