#1 ⟨
a
,
b
|
aa
=1⟩
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Monoids with two generators and one relation
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#2
⟨
a
,
b
|
ab
=1⟩
Quick links
Properties
Rewriting system
Other submonoids of same group
Properties
Presentation has sum-of-sides 2
Isomorphic to ℤ
2
∗ ℕ
Infinite cancellative non-commutative monoid
Submonoid of enveloping group: ⟨
a
,
b
|
aa
⟩
Embedding:
φ
(
a
) =
a
,
φ
(
b
) =
b
Rewriting system
Format:
Pretty
Plain
Word to reduce:
Tips:
Lowercase letters stand for generators.
Spaces are ignored.
Numbers repeat the previous letter, e.g.
b90
.
Reduction strategy:
Leftmost
Rightmost
Path to normal form:
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
2
⇒ 1
[1]
# ab:aa=1 ab aa=1
Other submonoids of same group
1 unique, 6 total
Σ
#
Presentation
Description
Related
6
69
⟨
a
,
b
|
abaaba
=1⟩
Isomorphic to ℤ
2
∗ ℤ
5 iso