#461 ⟨
a
,
b
|
aaaa
=1,
bbbb
=1⟩
Up:
Monoids with two generators and two relations
Prev:
#458
⟨
a
,
b
|
aaaa
=1,
abbb
=1⟩
Next:
#484
⟨
a
,
b
|
aabb
=1,
abab
=1⟩
Properties
Presentation has sum-of-sides 8
Isomorphic to ℤ
4
∗ ℤ
4
Infinite non-Abelian group
Inverses of generators:
a
-1
=
a
3
b
-1
=
b
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
4
⇒ 1
b
4
⇒ 1
# ab:aaaa=1,bbbb=1 ab aaaa=1 bbbb=1
Right Cayley graph (truncated)
Left Cayley graph (truncated)
Other isomorphic instances
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
1 total
Σ
#
Presentation
Mapping
10
5720
⟨
a
,
b
|
aaaa
=1,
abbbb
=
a
⟩
φ
(
a
) =
a
,
φ
(
b
) =
b
