#704 ⟨a, b | abaabaaba=1⟩

Up:Monoids with two generators and one relation
Prev:#701 ⟨a, b | abaaabbab=1⟩
Next:#731 ⟨a, b | aaaaaaaa=a⟩

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. b(a2b)2a ⇒ ab(a2b)2 [2]
2. (a2b)3 ⇒ 1 [4]
# ab:abaabaaba=1 ab
baabaaba=abaabaab
aabaabaab=1

Other submonoids of same group

1 unique, 1 total

Σ#PresentationDescriptionRelated
33⟨a, b | aaa=1⟩Isomorphic to ℤ3 ∗ ℕ