#1408 ⟨a, b | aabaababba=1⟩
Properties
- Presentation has sum-of-sides 10
- Infinite non-Abelian group
- Group inverses:
- a-1 = bcbda
- b-1 = cbdc
- c-1 = bcbd
- d-1 = (cb)2
Complete rewriting system
- Reduction order:
- Right-to-left recursive path with deg(d) = deg(b) = deg(c) = 0, d < b < c; deg(a) = 1
- Auxiliary generator: aa=c
- Auxiliary generator: abba=d
- dcb ⇒ cbd
- (cb)2d ⇒ 1
- bcbdc ⇒ 1
- ad ⇒ cb2a
- ac ⇒ ca
- abd ⇒ b2cab
- ab2 ⇒ dbcbda
- abc ⇒ b(dc2b)2cbab
- a2 ⇒ c
# ab:aabaababba=1 reversed:dbc/a aa=c,abba=d frequency:2/1,4/5
dcb=cbd
cbcbd=1
bcbdc=1
ad=cbba
ac=ca
abd=bbcab
abb=dbcbda
abc=bdccbdccbcbab
aa=c
Right Cayley graph (truncated)
Left Cayley graph (truncated)
Other isomorphic instances
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
1 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 1426 | ⟨a, b | aababbaaab=1⟩ | φ(a) = a, φ(b) = b |