#6268 ⟨
a
,
b
,
c
|
aa
=1,
bcbbcb
=1⟩
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Monoid enumeration
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#6267
⟨
a
,
b
,
c
|
aa
=1,
bcbbbc
=1⟩
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#6269
⟨
a
,
b
,
c
|
aa
=1,
bcbcbc
=1⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 8
Infinite non-Abelian group
Element
ba
has infinite order
Inverses of generators:
a
-1
=
a
b
-1
=
bc
b
2
c
c
-1
=
b
2
c
b
2
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.
a
2
⇒ 1
[1]
2.
c
b
2
cb
⇒
bc
b
2
c
[3]
3.
(
b
2
c
)
2
⇒ 1
[5]
# abc:aa=1,bcbbcb=1 abc - - aa=1 cbbcb=bcbbc bbcbbc=1