#820 ⟨a, b | aabbabba=b⟩

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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. a2b2ab3 ⇒ ba(b2a)2 [2]
2. a2(b2a)2 ⇒ b [1]
# ab:aabbabba=b ba
aabbabbb=babbabba
aabbabba=b

Other submonoids of same group

1 unique, 14 total

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

Other submonoids of anti-isomorphic group

2 unique, 2 total

Σ#PresentationDescriptionRelated
102041⟨a, b | abaababa=bb⟩Infinite cancellative non-commutative monoid
102587⟨a, b | abaaba=babb⟩Infinite cancellative non-commutative monoid