#700 ⟨
a
,
b
|
abaaababa
=1⟩
Up:
Monoids with two generators and one relation
Prev:
#699
⟨
a
,
b
|
abaaabaab
=1⟩
Next:
#701
⟨
a
,
b
|
abaaabbab
=1⟩
Properties
Presentation has sum-of-sides 9
Infinite non-Abelian group
Group inverses:
a
-1
=
bcac
b
-1
= (
ca
)
2
c
-1
=
bca
c
3
a
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:
aab=c
c
2
a
2
⇒ (
ac
)
2
c
2
ac
⇒
a
b
(
ca
)
2
⇒ 1
ab
⇒
bca
c
2
cb
⇒
b
c
4
# ab:abaaababa=1 ac/b aab=c frequency:3/0 ccaa=acac ccac=a bcaca=1 ab=bcacc cb=bcccc
Right Cayley graph (truncated)
Left Cayley graph (truncated)
