#4218 ⟨
a
,
b
|
aaaaa
=1,
bbbbb
=1⟩
Up:
Monoids with two generators and two relations
Prev:
#4212
⟨
a
,
b
|
aaaaa
=1,
abbbb
=1⟩
Next:
#4274
⟨
a
,
b
|
aaabb
=1,
aabab
=1⟩
Properties
Presentation has sum-of-sides 10
Isomorphic to ℤ
5
∗ ℤ
5
Infinite non-Abelian group
Inverses of generators:
a
-1
=
a
4
b
-1
=
b
4
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
5
⇒ 1
# ab:aaaaa=1,bbbbb=1 ab aaaaa=1 bbbbb=1
Right Cayley graph (truncated)
Left Cayley graph (truncated)
