#1174 ⟨a, b | aaaba=baab⟩

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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. a3ba ⇒ ba2b [1]
2. a3b2a2b ⇒ b(a2b)2a [2]
# ab:aaaba=baab ba
aaaba=baab
aaabbaab=baabaaba

Other submonoids of same group

6 unique, 24 total

Σ#PresentationDescriptionRelated
7207⟨a, b | aaaba=bb⟩Infinite cancellative non-commutative monoid
8504⟨a, b | aaaba=bab⟩Infinite cancellative non-commutative monoid
9670⟨a, b | aabababba=1⟩Infinite non-Abelian group8 iso, 10 anti-iso
9850⟨a, b | abababba=b⟩Infinite cancellative non-commutative monoid
114828⟨a, b | abababba=bab⟩Infinite cancellative non-commutative monoid
115942⟨a, b | abbbba=babbb⟩Infinite cancellative non-commutative monoid

Other submonoids of anti-isomorphic group

6 unique, 6 total

Σ#PresentationDescriptionRelated
7174⟨a, b | aaabba=b⟩Infinite cancellative non-commutative monoid
8362⟨a, b | aaababa=b⟩Infinite cancellative non-commutative monoid
9765⟨a, b | aaabaaba=b⟩Infinite cancellative non-commutative monoid
101612⟨a, b | aaabaaaba=b⟩Infinite cancellative non-commutative monoid
102742⟨a, b | baaab=aaaba⟩Infinite cancellative non-commutative monoid
113430⟨a, b | aaabaaaaba=b⟩Infinite cancellative non-commutative monoid