#3585 ⟨
a
,
b
,
c
|
ba
=
ab
,
ca
=
bc
⟩
Up:
Monoid enumeration
Prev:
#3584
⟨
a
,
b
,
c
|
ba
=
ab
,
ca
=
ac
⟩
Next:
#3586
⟨
a
,
b
,
c
|
ba
=
ab
,
cc
=
aa
⟩
Contents
Properties
Rewriting system
Other submonoids of same group
Properties
Sum of relation sides is 8
Infinite cancellative non-commutative monoid
Element
a
has infinite order
Submonoid of enveloping group: ⟨
a
,
b
|
aaba
-1
b
-1
b
-1
a
-1
b
⟩
Embedding:
φ
(
a
) =
b
-1
abb
,
φ
(
b
) =
ab
,
φ
(
c
) =
b
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
⇒
ab
[1]
2.
ca
⇒
bc
[2]
# abc:ba=ab,ca=bc abc - - ba=ab ca=bc
Other submonoids of same group
1 unique, 1 total
Σ
#
Presentation
Properties
8
3426
⟨
a
,
b
,
c
|
ba
=
ab
,
acb
=
c
⟩
Can
Inf