#5730 ⟨
a
,
b
|
aaaa
=1,
bbabb
=
a
⟩
Up:
Monoids with two generators and two relations
Prev:
#5729
⟨
a
,
b
|
aaaa
=1,
babbb
=
b
⟩
Next:
#5731
⟨
a
,
b
|
aaaa
=1,
bbabb
=
b
⟩
Properties
Presentation has sum-of-sides 10
Infinite non-Abelian group
Inverses of generators:
a
-1
=
a
3
b
-1
=
b
a
3
ca
c
-1
=
a
3
ca
Complete rewriting system
Format:
Pretty
Plain
Word to reduce:
Tips:
Lowercase letters stand for generators.
Spaces are ignored.
Numbers repeat the previous letter, e.g.
b90
.
Reduction strategy:
Leftmost
Rightmost
Path to normal form:
1
1
Reduction order:
Left-to-right recursive path with deg(
a
) = deg(
c
) = 0,
a
<
c
; deg(
b
) = 1
Auxiliary generator:
bb=c
c
a
2
⇒
a
2
c
cac
⇒
a
a
4
⇒ 1
cb
⇒
bc
cab
⇒
ab
a
3
ca
b
2
⇒
c
# ab:aaaa=1,bbabb=a ac/b bb=c frequency:2/0 caa=aac cac=a aaaa=1 cb=bc cab=abaaaca bb=c
Right Cayley graph (truncated)
Left Cayley graph (truncated)
