#4658 ⟨a, b | aaab=a, abba=b⟩

Quick links

1. Properties
2. Staircase diagram
3. Rewriting system
4. Isomorphic instances

Properties

• Presentation has sum-of-sides 10
• Infinite non-cancellative commutative monoid
• Not cancellative, because multiplication by ab is not injective:
  • ab ⋅ a²b = ab and ab ⋅ 1 = ab, however a²b ≠ 1
• Commutative Gröbner basis: ⟨a, b | a³b=a, a²b²=b⟩
• Cancellative quotient is isomorphic to ℤ
• Enveloping group is isomorphic to ℤ
• Group of units is isomorphic to ℤ₁
• 2 Archimedian components:
  • 1, b

Staircase diagram

Rewriting system

1

# ab:aaab=a,abba=b ab
ba=ab
aaab=a
aabb=b

Isomorphic instances

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