#13308 ⟨
a
,
b
|
aaaaa
=1,
bbbbbb
=1⟩
Up:
Monoids with two generators and two relations
Prev:
#13295
⟨
a
,
b
|
aaaaa
=1,
abbabb
=1⟩
Next:
#13340
⟨
a
,
b
|
aaaab
=1,
abbbbb
=1⟩
Properties
Presentation has sum-of-sides 11
Isomorphic to ℤ
5
∗ ℤ
6
Infinite non-Abelian group
Inverses of generators:
a
-1
=
a
4
b
-1
=
b
5
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
5
⇒ 1
b
6
⇒ 1
# ab:aaaaa=1,bbbbbb=1 ab aaaaa=1 bbbbbb=1
Right Cayley graph (truncated)
Left Cayley graph (truncated)
