#30 ⟨
a
,
b
|
aabba
=1⟩
Up:
Monoids with two generators and one relation
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#29
⟨
a
,
b
|
aabab
=1⟩
Next:
#33
⟨
a
,
b
|
abbba
=1⟩
Properties
Presentation has sum-of-sides 5
Infinite non-Abelian group
Group inverses:
a
-1
=
a
2
d
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:
aaa=c
Auxiliary generator:
bb=d
b
2
⇒
d
ca
⇒
ac
cb
⇒
bc
cd
⇒ 1
da
⇒
ad
db
⇒
bd
dc
⇒ 1
a
3
⇒
c
# ab:aabba=1 abcd aaa=c,bb=d magic:0 bb=d ca=ac cb=bc cd=1 da=ad db=bd dc=1 aaa=c
Right Cayley graph (truncated)
Left Cayley graph (truncated)
