#1378 ⟨a, b | aaabbbaaab=1⟩
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- Properties
- Rewriting system
- Isomorphic instances
- Presentation has sum-of-sides 10
- Infinite non-Abelian group
- Inverses of generators:
- a-1 = a2db2
- b-1 = bdc
- c-1 = db2
- d-1 = b2c
- Reduced group presentation: ⟨a, b | aaabaaabbb⟩
- Isomorphism: φ(a) = a, φ(b) = b
- Auxiliary generators:
- c = aaa
- d = bcb
- Reduction order:
- Right-to-left recursive path with deg(d) = 0; deg(c) = deg(b) = deg(a) = 1, c < b < a
- Certificate: derivations of all rewriting rules from the defining relations.
- Morphocompletion: how the auxiliary generators were found.
# ab:aaabbbaaab=1 reversed:d/cba aaa=c,bcb=d morph:3/0,3/0
cd=dc
dbd=b
cb=bddc
bbd=dbb
ca=ac
dbbc=1
dbba=adbb
aaa=c
bbbc=db
bbba=dbadbb
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
3 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 1402 | ⟨a, b | aabaaabbba=1⟩ | φ(a) = a, φ(b) = b |
| 10 | 1458 | ⟨a, b | aabbbaaaba=1⟩ | φ(a) = a, φ(b) = b |
| 10 | 1465 | ⟨a, b | aabbbabbba=1⟩ | φ(a) = b, φ(b) = a |