#3 ⟨
a
,
b
|
aaa
=1⟩
Up:
Monoid enumeration
Prev:
#2
⟨
a
,
b
|
ab
=1⟩
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#4
⟨
a
,
b
|
aab
=1⟩
Contents
Properties
Rewriting system
Other submonoids of same group
Properties
Sum of relation sides is 3
Isomorphic to ℤ
3
∗ ℕ
Infinite cancellative non-commutative monoid
Element
a
2
b
has infinite order
Submonoid of enveloping group: ⟨
a
,
b
|
aaa
⟩
Embedding:
φ
(
a
) =
a
,
φ
(
b
) =
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
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
a
3
⇒ 1
[1]
# ab:aaa=1 ab - - aaa=1
Other submonoids of same group
1 unique, 1 total
Σ
#
Presentation
Properties
Description
9
704
⟨
a
,
b
|
abaabaaba
=1⟩
Grp
Inf
ℤ
3
∗ ℤ