#717 ⟨a, b | ababbabba=1⟩
Properties
- Presentation has sum-of-sides 9
- Infinite non-Abelian group
- Group inverses:
- a-1 = d(db)2
- b-1 = c(bd)2
- c-1 = b(db)2
- d-1 = cbdbd3bdb
Complete rewriting system
- Reduction order:
- Left-to-right recursive path with deg(d) = deg(b) = 0, d < b; deg(c) = deg(a) = 1, c < a
- Auxiliary generator: aa=c
- Auxiliary generator: ab=d
- d2(bd)2 ⇒ b
- (bd)3 ⇒ d2bdb2
- d4bdb2 ⇒ b2d
- bd3bdb2 ⇒ d2bdb3d
- cb(db)2 ⇒ 1
- cd2bdb2 ⇒ d
- dc ⇒ cd2bd3
- bc ⇒ cbdbd3
- a ⇒ cd(db)2
# ab:ababbabba=1 db/ca aa=c,ab=d frequency:2/3,2/0
ddbdbd=b
bdbdbd=ddbdbb
ddddbdbb=bbd
bdddbdbb=ddbdbbbd
cbdbdb=1
cddbdbb=d
dc=cddbddd
bc=cbdbddd
a=cddbdb
Right Cayley graph (truncated)
Left Cayley graph (truncated)
