#340 ⟨
a
,
b
|
abbbbbba
=1⟩
Up:
Monoids with two generators and one relation
Prev:
#339
⟨
a
,
b
|
abbbaaab
=1⟩
Next:
#341
⟨
a
,
b
|
aaaaaaa
=
a
⟩
Properties
Presentation has sum-of-sides 8
Infinite non-Abelian group
Group inverses:
a
-1
=
ad
b
-1
=
b
5
c
c
-1
=
d
d
-1
=
c
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 shortlex with
a
<
b
<
c
<
d
Auxiliary generator:
aa=c
Auxiliary generator:
bbbbbb=d
a
2
⇒
c
ca
⇒
ac
cb
⇒
bc
cd
⇒ 1
da
⇒
ad
db
⇒
bd
dc
⇒ 1
b
6
⇒
d
# ab:abbbbbba=1 abcd aa=c,bbbbbb=d magic:0 aa=c ca=ac cb=bc cd=1 da=ad db=bd dc=1 bbbbbb=d
Right Cayley graph (truncated)
Left Cayley graph (truncated)
