#489 ⟨a, b | aaaaa=bab⟩

Up:Monoids with two generators and one relation
Prev:#488 ⟨a, b | aaaaa=abb⟩
Next:#490 ⟨a, b | aaaaa=bbb⟩

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. a6b ⇒ ba6 [2]
2. bab ⇒ a5 [1]
# ab:aaaaa=bab a/b
aaaaaab=baaaaaa
bab=aaaaa

Other submonoids of same group

6 unique, 13 total

Σ#PresentationDescriptionRelated
8275⟨a, b | aaaaabba=1⟩Infinite non-Abelian group7 iso
8412⟨a, b | abbbbba=b⟩Infinite cancellative non-commutative monoid
8415⟨a, b | aaaaaa=bb⟩Infinite cancellative non-commutative monoid
8484⟨a, b | abbbba=bb⟩Infinite cancellative non-commutative monoid
8556⟨a, b | abbba=bbb⟩Infinite cancellative non-commutative monoid
8585⟨a, b | baab=aaaa⟩Infinite cancellative non-commutative monoid