#5622 ⟨
a
,
b
|
abab
=1,
aaaaaa
=1⟩
Up:
Monoids with two generators and two relations
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#5605
⟨
a
,
b
|
aabb
=1,
ababab
=1⟩
Next:
#5625
⟨
a
,
b
|
abab
=1,
aaaabb
=1⟩
Properties
Presentation has sum-of-sides 10
Infinite non-Abelian group
Inverses of generators:
a
-1
=
a
5
b
-1
=
aba
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 recursive path with deg(
a
) = 0; deg(
b
) = 1
a
6
⇒ 1
bab
⇒
a
5
# ab:abab=1,aaaaaa=1 a/b aaaaaa=1 bab=aaaaa
Right Cayley graph (truncated)
Left Cayley graph (truncated)
