#1821 ⟨a, b | aaaaaaaa=bb⟩

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Quick links

  1. Properties
  2. Rewriting system
  3. Other submonoids of same 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. b2a ⇒ ab2 [2]
2. a8 ⇒ b2 [1]
# ab:aaaaaaaa=bb ab
bba=abb
aaaaaaaa=bb

Other submonoids of same group

8 unique, 12 total

Σ#PresentationDescriptionRelated
101281⟨a, b | aaaaaaabba=1⟩Infinite non-Abelian group4 iso
101818⟨a, b | abbbbbbba=b⟩Infinite cancellative non-commutative monoid
102090⟨a, b | abbbbbba=bb⟩Infinite cancellative non-commutative monoid
102095⟨a, b | aaaaaaa=bab⟩Infinite cancellative non-commutative monoid
102362⟨a, b | abbbbba=bbb⟩Infinite cancellative non-commutative monoid
102370⟨a, b | aaaaaa=baab⟩Infinite cancellative non-commutative monoid
102634⟨a, b | abbbba=bbbb⟩Infinite cancellative non-commutative monoid
102741⟨a, b | baaab=aaaaa⟩Infinite cancellative non-commutative monoid