Back
〈
a
,
b
|
aaa
=
1
,
babbbbb
=
a
〉
Monoid presentation of length 11
Properties
Finite non-Abelian group with 378 elements
Completion parameters
Reduction order: right-to-left a/b
Inverses of generators
a
-1
=
a
2
b
-1
=
b
4
aba
2
Complete rewriting system
a
3
⇒ 1
ba
2
ba
⇒
a(ab)
2
baba
2
⇒
aba
2
b
ba
2
b
2
a
⇒
a
2
b
2
ab
(ba)
3
⇒
(ab)
3
bab
2
a
2
⇒
ab
2
a
2
b
ba
2
b
3
a
⇒
a
2
b
3
ab
(ba)
2
b
2
a
⇒
a(bab)
2
(bab)
2
a
⇒
ab
2
(ab)
2
bab
3
a
2
⇒
ab
3
a
2
b
b
5
a
⇒
a
2
b
4
a
2
b
bab
4
a
⇒
a
2
b
5
ba
2
b
4
a
⇒
a
2
b
4
ab
(ba)
2
b
3
a
⇒
abab
3
ab
ba(b
2
a)
2
⇒
a(b
2
a)
2
b
bab
3
aba
⇒
ab
3
(ab)
2
bab
5
⇒
a
bab
2
ab
3
a
⇒
a(b
2
ab)
2
(bab
2
)
2
a
⇒
ab(b
2
a)
2
b
ba(b
3
a)
2
⇒
a(b
3
a)
2
b
b
10
⇒
abab
3
a
b
4
a
2
b
6
⇒
ab
4
a
Right Cayley graph
Left Cayley graph
Others with same cardinality
1 unique, 1 total
Length:
Presentation:
Description:
Related:
11
〈
a
,
b
|
aaba
=
b
,
bbbbbb
=
1
〉
Finite non-Abelian group with 378 elements
