#5857 ⟨a, b | abaaba=babab⟩

Up:Monoids with two generators and one relation
Prev:#5856 ⟨a, b | abaaba=baabb⟩
Next:#5858 ⟨a, b | abaaba=babbb⟩

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. bcb ⇒ c2 [4]
2. c3b ⇒ bc3 [6]
3. cba ⇒ abc [5]
4. c2a ⇒ babc [7]
5. aba ⇒ c [2]
# ab:abaaba=babab bc/a aba=c morph:3/0
bcb=cc
cccb=bccc
cba=abc
cca=babc
aba=c

Other submonoids of same group

7 unique, 23 total

Σ#PresentationDescriptionRelated
7139⟨a, b | aaabbba=1⟩Infinite non-Abelian group16 iso
7238⟨a, b | aaaa=bbb⟩Infinite cancellative non-commutative monoid
8550⟨a, b | ababa=bbb⟩Infinite cancellative non-commutative monoid
9988⟨a, b | abababa=bb⟩Infinite cancellative non-commutative monoid
9999⟨a, b | abbabba=bb⟩Infinite cancellative non-commutative monoid
101816⟨a, b | abbbabbba=b⟩Infinite cancellative non-commutative monoid
113820⟨a, b | abbabbabba=b⟩Infinite cancellative non-commutative monoid