#20448 ⟨
a
,
b
|
ba
=
ab
,
aaaaaaa
=1⟩
Up:
Monoids with two generators and two relations
Prev:
#20318
⟨
a
,
b
|
aba
=
b
,
bbbb
=
bab
⟩
Next:
#20520
⟨
a
,
b
|
ab
=
aa
,
aaaaaa
=
a
⟩
Properties
Presentation has sum-of-sides 11
Isomorphic to ℤ
7
⊕ ℕ
Infinite cancellative commutative monoid
Commutative Gröbner basis: ⟨
a
,
b
|
a
7
=1⟩
Grothendieck group is isomorphic to ℤ
7
⊕ ℤ
Inverses of generators:
a
-1
=
a
6
Group of units is isomorphic to ℤ
7
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
7
⇒ 1
# ab:ba=ab,aaaaaaa=1 ab ba=ab aaaaaaa=1
Staircase diagram
Right Cayley graph (truncated)
