#2041 ⟨a, b | abaababa=bb⟩

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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. b(ba)3 ⇒ aba2b3 [2]
2. (aba)2ba ⇒ b2 [1]
3. b3a2(ba)2 ⇒ (aba)2b3 [3]
# ab:abaababa=bb ab
bbababa=abaabbb
abaababa=bb
bbbaababa=abaababbb

Other submonoids of same group

2 unique, 15 total

Σ#PresentationDescriptionRelated
9664⟨a, b | aabaabbba=1⟩Infinite non-Abelian group6 iso, 7 anti-iso
9820⟨a, b | aabbabba=b⟩Infinite cancellative non-commutative monoid

Other submonoids of anti-isomorphic group

1 unique, 1 total

Σ#PresentationDescriptionRelated
102587⟨a, b | abaaba=babb⟩Infinite cancellative non-commutative monoid