〈a, b | aaa=1, bbbb=aba〉

Monoid presentation of length 10

Properties

Finite non-commutative monoid with 1083 elements

Completion parameters

Reduction order: left-to-right b/a

Complete rewriting system

b⁹¹ ⇒ b
bab⁹⁰ ⇒ ba
b⁵a ⇒ ab⁵
a²b ⇒ bab⁸⁷
aba ⇒ b⁴
ab²a ⇒ b⁴ab⁴
ba² ⇒ b²ab⁸⁶
bab³a ⇒ ab⁴ab⁹
(b⁴a)² ⇒ ab³ab⁸⁶
a³ ⇒ 1

Idempotents

2 elements

1
b⁹⁰

Right Cayley graph

Left Cayley graph

Others with same cardinality

2 unique, 3 total

Length:	Presentation:	Description:	Related:
10	〈a, b \| aaa=1, abbbba=b〉	Finite non-commutative monoid with 1083 elements	1 isomorphic
11	〈a, b \| aaa=1, bbabb=aba〉	Finite non-commutative monoid with 1083 elements

Other isomorphic instances

1 total

Length:	Presentation:
11	〈a, b \| aaa=1, aabbbb=ba〉