#1425 ⟨a, b | aabababbba=1⟩
Properties
- Presentation has sum-of-sides 10
- Infinite non-Abelian group
- Group inverses:
- a-1 = eb
- b-1 = cdcb
- c-1 = e
- d-1 = e(eb)2
- e-1 = c
Complete rewriting system
- Reduction order:
- Right-to-left recursive path with deg(c) = 0; deg(d) = deg(e) = 1, d < e; deg(b) = deg(a) = 2, b < a
- Auxiliary generator: ba=c
- Auxiliary generator: aac=d
- Auxiliary generator: dcbb=e
- ce ⇒ 1
- ec ⇒ 1
- dcbc ⇒ ede2b
- dede2bc2 ⇒ (cdc)2b
- bd ⇒ cde2bc
- bcdc ⇒ cdcb
- dcbe ⇒ ebcd
- de2be ⇒ cdcb
- a ⇒ de2b
- dcb2 ⇒ e
- b2c ⇒ e3beb
- de2bc2bc ⇒ ebede2b
- dede2bcbe ⇒ cdc2dc4b2
- de2bc2be ⇒ (eb)2cd
- bcdbe ⇒ cdc4b2
- (be)2 ⇒ c3b2
- de2bc2b2 ⇒ ebe
- b3e ⇒ e3bc2b2
# ab:aabababbba=1 reversed:c/de/ba ba=c,aac=d,dcbb=e frequency:2/0,3/5,4/1
ce=1
ec=1
dcbc=edeeb
dedeebcc=cdccdcb
bd=cdeebc
bcdc=cdcb
dcbe=ebcd
deebe=cdcb
a=deeb
dcbb=e
bbc=eeebeb
deebccbc=ebedeeb
dedeebcbe=cdccdccccbb
deebccbe=ebebcd
bcdbe=cdccccbb
bebe=cccbb
deebccbb=ebe
bbbe=eeebccbb
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 | 1463 | ⟨a, b | aabbbababa=1⟩ | φ(a) = b, φ(b) = deeb |