#1948 ⟨
a
,
b
,
c
|
abc
=
ab
,
cca
=1⟩
Up:
Monoid enumeration
Prev:
#1946
⟨
a
,
b
,
c
|
abc
=
ab
,
cbb
=1⟩
Next:
#1949
⟨
a
,
b
,
c
|
abc
=
ab
,
ccb
=1⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 8
Infinite non-cancellative non-commutative monoid
Element
a
has infinite order
Not left cancellative, because left multiplication by
b
is not injective:
b
⋅
a
=
b
and
b
⋅ 1 =
b
, however
a
≠ 1
Not right cancellative, because right multiplication by
ca
is not injective:
cac
⋅
ca
=
ca
and 1 ⋅
ca
=
ca
, however
cac
≠ 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.
ba
⇒
b
[4]
2.
bc
⇒
b
[3]
3.
c
2
a
⇒ 1
[2]
# abc:abc=ab,cca=1 abc - - ba=b bc=b cca=1