#14 ⟨
a
,
b
|
abba
=1⟩
Up:
Monoids with two generators and one relation
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#13
⟨
a
,
b
|
abab
=1⟩
Next:
#15
⟨
a
,
b
|
aaa
=
a
⟩
Properties
Presentation has sum-of-sides 4
Infinite non-Abelian group
Group inverses:
a
-1
=
ad
b
-1
=
bc
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:
bb=d
a
2
⇒
c
b
2
⇒
d
ca
⇒
ac
cb
⇒
bc
cd
⇒ 1
da
⇒
ad
db
⇒
bd
dc
⇒ 1
# ab:abba=1 abcd aa=c,bb=d magic:0 aa=c bb=d ca=ac cb=bc cd=1 da=ad db=bd dc=1
Right Cayley graph (truncated)
Left Cayley graph (truncated)
