#237 ⟨a, b | aaaa=bab⟩

Up:Monoids with two generators and one relation
Prev:#236 ⟨a, b | aaaa=abb⟩
Next:#238 ⟨a, b | aaaa=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. a5b ⇒ ba5 [2]
2. bab ⇒ a4 [1]
# ab:aaaa=bab a/b
aaaaab=baaaaa
bab=aaaa

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
7199⟨a, b | aaaaa=bb⟩Infinite cancellative non-commutative monoid
7232⟨a, b | abbba=bb⟩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