#5944 ⟨a, b | abbbba=bbbbb⟩

Up:Monoids with two generators and one relation
Prev:#5943 ⟨a, b | abbbba=bbabb⟩

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. ab4a ⇒ b5 [1]
2. b9a ⇒ ab9 [2]
# ab:abbbba=bbbbb ab
abbbba=bbbbb
bbbbbbbbba=abbbbbbbbb

Other submonoids of same group

9 unique, 13 total

Σ#PresentationDescriptionRelated
112783⟨a, b | aaaaaaaabba=1⟩Infinite non-Abelian group4 iso
113832⟨a, b | abbbbbbbba=b⟩Infinite cancellative non-commutative monoid
113835⟨a, b | aaaaaaaaa=bb⟩Infinite cancellative non-commutative monoid
114360⟨a, b | abbbbbbba=bb⟩Infinite cancellative non-commutative monoid
114365⟨a, b | aaaaaaaa=bab⟩Infinite cancellative non-commutative monoid
114888⟨a, b | abbbbbba=bbb⟩Infinite cancellative non-commutative monoid
114896⟨a, b | aaaaaaa=baab⟩Infinite cancellative non-commutative monoid
115416⟨a, b | abbbbba=bbbb⟩Infinite cancellative non-commutative monoid
115431⟨a, b | aaaaaa=baaab⟩Infinite cancellative non-commutative monoid