#727 ⟨a, b | abbabbbba=1⟩
Properties
- Presentation has sum-of-sides 9
- Infinite non-Abelian group
- Group inverses:
- a-1 = bdb3d
- b-1 = cbdb3
- c-1 = bdb4
- d-1 = cbdb3dbdb3
Complete rewriting system
- Reduction order:
- Left-to-right recursive path with deg(d) = 0; deg(b) = 1; deg(c) = deg(a) = 2, c < a
- Auxiliary generator: aa=c
- Auxiliary generator: ba=d
- dbdb3d ⇒ b
- dbdb4 ⇒ b2db3d
- cbdb4 ⇒ 1
- dc ⇒ cbd2(bd)2
- bc ⇒ cbd2bdb2
- a ⇒ cbdb3d
# ab:abbabbbba=1 d/b/ca aa=c,ba=d frequency:2/3,2/2
dbdbbbd=b
dbdbbbb=bbdbbbd
cbdbbbb=1
dc=cbddbdbd
bc=cbddbdbb
a=cbdbbbd
Right Cayley graph (truncated)
Left Cayley graph (truncated)