#404 ⟨a, b | abababa=b⟩

Up:Monoids with two generators and one relation
Prev:#403 ⟨a, b | abababa=a⟩
Next:#405 ⟨a, b | ababbba=a⟩

Quick links

  1. Properties
  2. Rewriting system
  3. Other submonoids of same group
  4. Isomorphic instances

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. a(ba)3 ⇒ b [1]
# ab:abababa=b ab
bba=abb
abababa=b

Other submonoids of same group

8 unique, 27 total

Σ#PresentationDescriptionRelated
660⟨a, b | aaabba=1⟩Infinite non-Abelian group19 iso
693⟨a, b | abbba=b⟩Infinite cancellative non-commutative monoid
696⟨a, b | aaaa=bb⟩Infinite cancellative non-commutative monoid
6113⟨a, b | abba=bb⟩Infinite cancellative non-commutative monoid
6122⟨a, b | bab=aaa⟩Infinite cancellative non-commutative monoid
8549⟨a, b | ababa=bab⟩Infinite cancellative non-commutative monoid
102355⟨a, b | abbabba=bab⟩Infinite cancellative non-commutative monoid
102586⟨a, b | abaaba=baab⟩Infinite cancellative non-commutative monoid

Isomorphic instances

The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.

1 total

Σ#PresentationMapping
101766⟨a, b | abaabaaba=b⟩φ(a) = a, φ(b) = ababab