#9519 ⟨
a
,
b
|
aa
=1,
bbbbbbbb
=1⟩
Up:
Monoids with two generators and two relations
Prev:
#9478
⟨
a
,
b
|
aa
=1,
abbbabbb
=1⟩
Next:
#9733
⟨
a
,
b
|
aa
=1,
abababb
=
b
⟩
Properties
Presentation has sum-of-sides 10
Isomorphic to ℤ
2
∗ ℤ
8
Infinite non-Abelian group
Inverses of generators:
a
-1
=
a
b
-1
=
b
7
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
2
⇒ 1
b
8
⇒ 1
# ab:aa=1,bbbbbbbb=1 ab aa=1 bbbbbbbb=1
Right Cayley graph (truncated)
Left Cayley graph (truncated)
