#618 ⟨a, b | ba=ab, aaaa=1⟩
Contents
- Properties
- Commutative structure
- Staircase diagram
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 8
- Isomorphic to ℤ4 ⊕ ℕ
- Infinite cancellative commutative monoid
- Element b has infinite order
- Gröbner basis: ⟨a, b | a4=1⟩
- Enveloping group is isomorphic to ℤ4 ⊕ ℤ
- Inverses of generators:
- Group of units is isomorphic to ℤ4
- 2 Archimedian components:
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:ba=ab,aaaa=1 ab - -
ba=ab
aaaa=1
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
2 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 4022 | ⟨a, b | aba=aab, aaaa=1⟩ | φ(a) = a, φ(b) = b |
| 10 | 5699 | ⟨a, b | aaaa=1, aaaba=b⟩ | φ(a) = a, φ(b) = b |