#21192 ⟨
a
,
b
|
aaa
=1,
abababab
=1⟩
Up:
Monoids with two generators and two relations
Prev:
#21112
⟨
a
,
b
|
bb
=
aa
,
abab
=
aba
⟩
Next:
#21200
⟨
a
,
b
|
aaa
=1,
ababbbbb
=1⟩
Properties
Presentation has sum-of-sides 11
Infinite non-Abelian group
Inverses of generators:
a
-1
=
a
2
b
-1
=
a
(
ba
)
3
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
a
3
⇒ 1
b
(
ab
)
3
⇒
a
2
# ab:aaa=1,abababab=1 ab aaa=1 bababab=aa
Right Cayley graph (truncated)
Left Cayley graph (truncated)
