#7120 ⟨
a
,
b
|
ba
=
ab
,
aaaa
=
bb
⟩
Up:
Monoids with two generators and two relations
Prev:
#7119
⟨
a
,
b
|
ba
=
ab
,
aaaa
=
ab
⟩
Next:
#7121
⟨
a
,
b
|
ba
=
ab
,
aaab
=
aa
⟩
Properties
Presentation has sum-of-sides 10
Isomorphic to ⟨(0, 1), (1, 2)⟩ ⊂ ℤ
2
⊕ ℤ
Infinite cancellative commutative monoid
Commutative Gröbner basis: ⟨
a
,
b
|
b
2
=
a
4
⟩
Grothendieck group is isomorphic to ℤ
2
⊕ ℤ
Group of units is isomorphic to ℤ
1
2 Archimedian components:
1,
b
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
ba
⇒
ab
a
4
⇒
b
2
# ab:ba=ab,aaaa=bb ab ba=ab aaaa=bb
Staircase diagram
Right Cayley graph (truncated)
