#1147 ⟨a, b | aaaaa=babb⟩

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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. a6b2 ⇒ baba5 [2]
2. bab2 ⇒ a5 [1]
# ab:aaaaa=babb a/b
aaaaaabb=babaaaaa
babb=aaaaa

Other submonoids of same group

3 unique, 9 total

Σ#PresentationDescriptionRelated
101297⟨a, b | aaaaababba=1⟩Infinite non-Abelian group3 iso, 3 anti-iso
102614⟨a, b | ababba=bbbb⟩Infinite cancellative non-commutative monoid
114878⟨a, b | abbabbba=bbb⟩Infinite cancellative non-commutative monoid

Other submonoids of anti-isomorphic group

1 unique, 1 total

Σ#PresentationDescriptionRelated
9830⟨a, b | aabbbbba=b⟩Infinite cancellative non-commutative monoid