#6910 ⟨
a
,
b
|
ba
=
ab
,
aaaaaa
=1⟩
Up:
Monoid enumeration
Prev:
#6845
⟨
a
,
b
|
bab
=
b
,
bbb
=
bab
⟩
Next:
#6917
⟨
a
,
b
|
ba
=
ab
,
aaabbb
=1⟩
Contents
Properties
Commutative structure
Staircase diagram
Rewriting system
Properties
Sum of relation sides is 10
Isomorphic to ℤ
6
⊕ ℕ
Infinite cancellative commutative monoid
Element
b
has infinite order
Commutative structure
Gröbner basis: ⟨
a
,
b
|
a
6
=1⟩
Enveloping group is isomorphic to ℤ
6
⊕ ℤ
Inverses of generators:
a
-1
=
a
5
Group of units is isomorphic to ℤ
6
2 Archimedian components:
1,
b
Staircase diagram
Rewriting system
Format:
Pretty
Plain
Word:
Enter a word above to compute its normal form. Tips:
Lowercase letters stand for generators.
Spaces are ignored.
Numbers repeat the previous letter, e.g.
b90
.
Strategy:
Leftmost
Rightmost
Result:
1
1
Reduction order:
Left-to-right shortlex with
a
<
b
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
ba
⇒
ab
[1]
2.
a
6
⇒ 1
[2]
# ab:ba=ab,aaaaaa=1 ab - - ba=ab aaaaaa=1
