#486 ⟨a, b | aabb=1, baba=1⟩
Contents
- Properties
- Commutative structure
- Staircase diagram
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 8
- Isomorphic to ℤ2 ⊕ ℤ
- Infinite Abelian group
- Element a has infinite order
- Inverses of generators:
- Gröbner basis: ⟨a, b | a2b2=1⟩
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:aabb=1,baba=1 ab - -
ba=ab
aabb=1
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
28 total
| Σ | # | Presentation | Mapping |
|---|
| 8 | 488 | ⟨a, b | abab=1, abba=1⟩ | φ(a) = a, φ(b) = b |
| 8 | 621 | ⟨a, b | ba=ab, aabb=1⟩ | φ(a) = a, φ(b) = b |
| 8 | 622 | ⟨a, b | ba=ab, abab=1⟩ | φ(a) = a, φ(b) = b |
| 8 | 623 | ⟨a, b | ba=ab, abba=1⟩ | φ(a) = a, φ(b) = b |
| 10 | 4028 | ⟨a, b | aba=aab, abba=1⟩ | φ(a) = a, φ(b) = b |
| 10 | 4031 | ⟨a, b | aba=aab, baab=1⟩ | φ(a) = a, φ(b) = b |
| 10 | 4032 | ⟨a, b | aba=aab, baba=1⟩ | φ(a) = a, φ(b) = b |
| 10 | 4034 | ⟨a, b | aba=aab, bbaa=1⟩ | φ(a) = a, φ(b) = b |
| 10 | 5885 | ⟨a, b | aabb=1, abbba=b⟩ | φ(a) = a, φ(b) = b |
| 10 | 5890 | ⟨a, b | aabb=1, babaa=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 5914 | ⟨a, b | abab=1, abbaa=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 5920 | ⟨a, b | abab=1, baaba=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 5924 | ⟨a, b | abab=1, bbaaa=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 5936 | ⟨a, b | abba=1, aabab=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 5944 | ⟨a, b | abba=1, ababa=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 5947 | ⟨a, b | abba=1, ababb=b⟩ | φ(a) = a, φ(b) = b |
| 10 | 5951 | ⟨a, b | abba=1, abbba=b⟩ | φ(a) = a, φ(b) = b |
| 10 | 5954 | ⟨a, b | abba=1, baaab=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 5959 | ⟨a, b | abba=1, babab=b⟩ | φ(a) = a, φ(b) = b |
| 10 | 6913 | ⟨a, b | ba=ab, aaaabb=1⟩ | φ(a) = b, φ(b) = aaab |
| 10 | 6915 | ⟨a, b | ba=ab, aaabab=1⟩ | φ(a) = b, φ(b) = aaab |
| 10 | 6916 | ⟨a, b | ba=ab, aaabba=1⟩ | φ(a) = b, φ(b) = aaab |
| 10 | 6918 | ⟨a, b | ba=ab, aabaab=1⟩ | φ(a) = b, φ(b) = aaab |
| 10 | 6919 | ⟨a, b | ba=ab, aababa=1⟩ | φ(a) = b, φ(b) = aaab |
| 10 | 6921 | ⟨a, b | ba=ab, aabbaa=1⟩ | φ(a) = b, φ(b) = aaab |
| 10 | 6924 | ⟨a, b | ba=ab, abaaab=1⟩ | φ(a) = b, φ(b) = aaab |
| 10 | 6925 | ⟨a, b | ba=ab, abaaba=1⟩ | φ(a) = b, φ(b) = aaab |
| 10 | 6929 | ⟨a, b | ba=ab, abbbba=1⟩ | φ(a) = aaab, φ(b) = b |