#1238 ⟨a, b | aabba=bbbb⟩

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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. a2b2a ⇒ b4 [1]
2. b4ab2a ⇒ a2b6 [2]
# ab:aabba=bbbb ab
aabba=bbbb
bbbbabba=aabbbbbb

Other submonoids of same group

3 unique, 10 total

Σ#PresentationDescriptionRelated
102342⟨a, b | ababbba=bbb⟩Infinite cancellative non-commutative monoid
112815⟨a, b | aaaaabaabba=1⟩Infinite non-Abelian group3 iso, 4 anti-iso
114350⟨a, b | abbabbbba=bb⟩Infinite cancellative non-commutative monoid

Other submonoids of anti-isomorphic group

2 unique, 2 total

Σ#PresentationDescriptionRelated
9966⟨a, b | aabbbba=bb⟩Infinite cancellative non-commutative monoid
101798⟨a, b | ababbbbba=b⟩Infinite cancellative non-commutative monoid