#631 ⟨a, b | aaabaabba=1⟩
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- Properties
- Rewriting system
- Other submonoids of same group
- Isomorphic instances
- Presentation has sum-of-sides 9
- Infinite non-Abelian group
- Inverses of generators:
- a-1 = dba
- b-1 = a2d
- c-1 = d
- d-1 = c
- Reduced group presentation: ⟨a, b | aabbab-1b-1⟩
- Isomorphism: φ(a) = b-1, φ(b) = bab
- Auxiliary generators:
- c = baa
- d = bcaa
- Reduction order:
- Left-to-right recursive path with deg(d) = deg(c) = 0, d < c; deg(a) = 1; deg(b) = 2
- Certificate: derivations of all rewriting rules from the defining relations.
- Morphocompletion: how the auxiliary generators were found.
# ab:aaabaabba=1 dc/a/b baa=c,bcaa=d morph:3/0,4/0
dc=1
cd=1
daa=aacc
caa=aadd
baa=c
cb=dbd
ddb=bc
adb=dba
5 unique, 5 total
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
5 total
| Σ | # | Presentation | Mapping |
|---|
| 9 | 641 | ⟨a, b | aaabbaaba=1⟩ | φ(a) = dba, φ(b) = aabaa |
| 9 | 662 | ⟨a, b | aabaabbaa=1⟩ | φ(a) = a, φ(b) = dbaabadba |
| 9 | 676 | ⟨a, b | aabbaaaab=1⟩ | φ(a) = a, φ(b) = dbadbaaba |
| 9 | 698 | ⟨a, b | abaaaabba=1⟩ | φ(a) = dba, φ(b) = aabaa |
| 9 | 727 | ⟨a, b | abbabbbba=1⟩ | φ(a) = aabaa, φ(b) = dba |