#1545 ⟨a, b | abbbbaaaab=1⟩
Properties
- Presentation has sum-of-sides 10
- Infinite non-Abelian group
- Group inverses:
- a-1 = db3d(ed)2
- b-1 = e
- c-1 = db3de2
- d-1 = db3(de)3
- e-1 = b
Complete rewriting system
- Reduction order:
- Left-to-right recursive path with deg(e) = 0; deg(b) = 1; deg(d) = 2; deg(a) = deg(c) = 3, a < c
- Auxiliary generator: bbaaa=c
- Auxiliary generator: ba=d
- Auxiliary generator: bcad=e
- be ⇒ 1
- eb ⇒ 1
- ed2 ⇒ db3de4
- bdb3d ⇒ d2b4
- bdb2d2 ⇒ d2b7de4
- e3db3d(ed)2 ⇒ d(ed)3b
- bd(ed)3 ⇒ e2db3(de)3
- d2b3d(ed)2 ⇒ b
- e3(db3d)2ed ⇒ d(ed)3bdb4
- (d2b3)2ded ⇒ bdb4
- e3(db3d)3 ⇒ d(ed)3b(db4)2
- (d2b3)3d ⇒ b(db4)2
- e3d(b3d2)2b2d2 ⇒ d(ed)3bdb4db7de4
- d2(b3d2)2b2d2 ⇒ bdb4db7de4
- a ⇒ ed
- c ⇒ bd(ed)2
# ab:abbbbaaaab=1 e/b/d/ac bbaaa=c,ba=d,bcad=e frequency:5/0,2/4,4/0
be=1
eb=1
edd=dbbbdeeee
bdbbbd=ddbbbb
bdbbdd=ddbbbbbbbdeeee
eeedbbbdeded=dedededb
bdededed=eedbbbdedede
ddbbbdeded=b
eeedbbbddbbbded=dedededbdbbbb
ddbbbddbbbded=bdbbbb
eeedbbbddbbbddbbbd=dedededbdbbbbdbbbb
ddbbbddbbbddbbbd=bdbbbbdbbbb
eeedbbbddbbbddbbdd=dedededbdbbbbdbbbbbbbdeeee
ddbbbddbbbddbbdd=bdbbbbdbbbbbbbdeeee
a=ed
c=bdeded
Right Cayley graph (truncated)
Left Cayley graph (truncated)
