#199 ⟨a, b | aaaaa=bb⟩

Up:Monoids with two generators and one relation
Prev:#198 ⟨a, b | aaaaa=ab⟩
Next:#200 ⟨a, b | aaaab=aa⟩

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. a5 ⇒ b2 [1]
# ab:aaaaa=bb ab
bba=abb
aaaaa=bb

Other submonoids of same group

7 unique, 18 total

Σ#PresentationDescriptionRelated
7131⟨a, b | aaaabba=1⟩Infinite non-Abelian group11 iso
7196⟨a, b | abbbba=b⟩Infinite cancellative non-commutative monoid
7232⟨a, b | abbba=bb⟩Infinite cancellative non-commutative monoid
7237⟨a, b | aaaa=bab⟩Infinite cancellative non-commutative monoid
7268⟨a, b | abba=bbb⟩Infinite cancellative non-commutative monoid
102333⟨a, b | abababa=bab⟩Infinite cancellative non-commutative monoid
102767⟨a, b | babab=ababa⟩Infinite cancellative non-commutative monoid