#1628 ⟨
a
,
b
,
c
|
aab
=
ab
,
cbc
=1⟩
Up:
Monoid enumeration
Prev:
#1627
⟨
a
,
b
,
c
|
aab
=
ab
,
cbb
=1⟩
Next:
#1629
⟨
a
,
b
,
c
|
aab
=
ab
,
cca
=1⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 8
Isomorphic to ℕ
(2 = 1)
∗ ℤ
Infinite non-cancellative non-commutative monoid
Element
ba
has infinite order
Not left cancellative, because left multiplication by
a
is not injective:
a
⋅
a
=
a
and
a
⋅ 1 =
a
, however
a
≠ 1
Not right cancellative, because right multiplication by
a
is not injective:
a
⋅
a
=
a
and 1 ⋅
a
=
a
, however
a
≠ 1
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
<
c
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
a
2
⇒
a
[5]
2.
cb
⇒
bc
[3]
3.
b
c
2
⇒ 1
[4]
# abc:aab=ab,cbc=1 abc - - aa=a cb=bc bcc=1