#4218 ⟨
a
,
b
|
aaaaa
=1,
bbbbb
=1⟩
Up:
Monoid enumeration
Prev:
#4212
⟨
a
,
b
|
aaaaa
=1,
abbbb
=1⟩
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#4274
⟨
a
,
b
|
aaabb
=1,
aabab
=1⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 10
Isomorphic to ℤ
5
∗ ℤ
5
Infinite non-Abelian group
Element
a
3
ba
has infinite order
Inverses of generators:
a
-1
=
a
4
b
-1
=
b
4
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
5
⇒ 1
[1]
2.
b
5
⇒ 1
[2]
# ab:aaaaa=1,bbbbb=1 ab - - aaaaa=1 bbbbb=1