#1076 ⟨a, b | aababa=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. a2(ba)2 ⇒ b3 [1]
2. b2(ba)3 ⇒ a2bab4 [2]
# ab:aababa=bbb ab
aababa=bbb
bbbababa=aababbbb

Other submonoids of same group

2 unique, 7 total

Σ#PresentationDescriptionRelated
9639⟨a, b | aaababbba=1⟩Infinite non-Abelian group3 iso, 2 anti-iso
114313⟨a, b | ababbabba=bb⟩Infinite cancellative non-commutative monoid

Other submonoids of anti-isomorphic group

1 unique, 1 total

Σ#PresentationDescriptionRelated
101965⟨a, b | aabababa=bb⟩Infinite cancellative non-commutative monoid