#681 ⟨a, b | aabbabaab=1⟩
Properties
- Presentation has sum-of-sides 9
- Infinite non-Abelian group
- Group inverses:
- a-1 = da
- b-1 = c(ca)2
- c-1 = dac(ca)2
- d-1 = a2
Complete rewriting system
- Reduction order:
- Left-to-right recursive path with deg(c) = deg(a) = 0, c < a; deg(d) = deg(b) = 1, d < b
- Auxiliary generator: ba=c
- Auxiliary generator: bccab=d
- c2(ac)2 ⇒ a
- (ac)3 ⇒ c2aca2
- c4aca2 ⇒ a2c
- ac3aca2 ⇒ c2aca3c
- da2 ⇒ 1
- dac2aca2 ⇒ c(ac)2
- cd ⇒ dc4ac
- ad ⇒ da
- b ⇒ dc4aca
# ab:aabbabaab=1 ca/db ba=c,bccab=d frequency:2/1,5/1
ccacac=a
acacac=ccacaa
ccccacaa=aac
acccacaa=ccacaaac
daa=1
daccacaa=cacac
cd=dccccac
ad=da
b=dccccaca
Right Cayley graph (truncated)
Left Cayley graph (truncated)
