#2398 ⟨a, b | aaaaba=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. ba2b ⇒ a4ba [1]
2. a(a3b)2 ⇒ ba6ba [2]
# ab:aaaaba=baab a/b
baab=aaaaba
aaaabaaab=baaaaaaba

Other submonoids of same group

5 unique, 10 total

Σ#PresentationDescriptionRelated
8423⟨a, b | aaaaba=bb⟩Infinite cancellative non-commutative monoid
91022⟨a, b | aaaaba=bab⟩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

4 unique, 4 total

Σ#PresentationDescriptionRelated
8354⟨a, b | aaaabba=b⟩Infinite cancellative non-commutative monoid
9752⟨a, b | aaaababa=b⟩Infinite cancellative non-commutative monoid
101584⟨a, b | aaaabaaba=b⟩Infinite cancellative non-commutative monoid
113371⟨a, b | aaaabaaaba=b⟩Infinite cancellative non-commutative monoid