#1936 ⟨a, b | aabaaaab=ab⟩

Quick links

1. Properties
2. Rewriting system

Properties

• Presentation has sum-of-sides 10
• Infinite non-cancellative non-commutative monoid
• Not left cancellative, because left multiplication by a is not injective:
  • a ⋅ aba⁴b = ab and a ⋅ b = ab, however aba⁴b ≠ b
• Not right cancellative, because right multiplication by b is not injective:
  • a²ba⁴ ⋅ b = ab and a ⋅ b = ab, however a²ba⁴ ≠ a
• Enveloping group is isomorphic to ℤ

Rewriting system

1

# ab:aabaaaab=ab ab
abaab=aabab
abaaab=aaabab
abaaaab=aaaabab
aaaaabab=ab