#1584 ⟨a, b | aaaabaaba=b⟩

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  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. a4ba2b2 ⇒ ba(a2b)2a [2]
2. a3(aba)2 ⇒ b [1]
# ab:aaaabaaba=b ba
aaaabaabb=baaabaaba
aaaabaaba=b

Other submonoids of same group

6 unique, 11 total

Σ#PresentationDescriptionRelated
8423⟨a, b | aaaaba=bb⟩Infinite cancellative non-commutative monoid
91022⟨a, b | aaaaba=bab⟩Infinite cancellative non-commutative monoid
102398⟨a, b | aaaaba=baab⟩Infinite cancellative non-commutative monoid
113068⟨a, b | aababababba=1⟩Infinite non-Abelian group2 iso, 3 anti-iso
113771⟨a, b | ababababba=b⟩Infinite cancellative non-commutative monoid
115486⟨a, b | aaaaba=baaab⟩Infinite cancellative non-commutative monoid

Other submonoids of anti-isomorphic group

3 unique, 3 total

Σ#PresentationDescriptionRelated
8354⟨a, b | aaaabba=b⟩Infinite cancellative non-commutative monoid
9752⟨a, b | aaaababa=b⟩Infinite cancellative non-commutative monoid
113371⟨a, b | aaaabaaaba=b⟩Infinite cancellative non-commutative monoid