#431 ⟨a, b | aaabaa=bb⟩

Up:Monoids with two generators and one relation
Prev:#430 ⟨a, b | aaabaa=ba⟩
Next:#432 ⟨a, b | aaabab=aa⟩

Quick links

  1. Properties
  2. Rewriting system
  3. Other submonoids of same group
  4. Other submonoids of anti-isomorphic 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. b2 ⇒ a3ba2 [1]
2. a(a2b)2 ⇒ ba3ba2 [2]
# ab:aaabaa=bb a/b
bb=aaabaa
aaabaab=baaabaa

Other submonoids of same group

5 unique, 10 total

Σ#PresentationDescriptionRelated
91038⟨a, b | aaabaa=bab⟩Infinite cancellative non-commutative monoid
102430⟨a, b | aaabaa=baab⟩Infinite cancellative non-commutative monoid
113070⟨a, b | aabababbaba=1⟩Infinite non-Abelian group1 iso, 4 anti-iso
113775⟨a, b | abababbaba=b⟩Infinite cancellative non-commutative monoid
115550⟨a, b | aaabaa=baaab⟩Infinite cancellative non-commutative monoid

Other submonoids of anti-isomorphic group

4 unique, 4 total

Σ#PresentationDescriptionRelated
8366⟨a, b | aaabbaa=b⟩Infinite cancellative non-commutative monoid
9769⟨a, b | aaababaa=b⟩Infinite cancellative non-commutative monoid
101616⟨a, b | aaabaabaa=b⟩Infinite cancellative non-commutative monoid
113434⟨a, b | aaabaaabaa=b⟩Infinite cancellative non-commutative monoid