〈a, b | aaa=1, abbbba=b〉

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 ⇒ b⁴a
ab³a ⇒ bab⁸⁶
ab⁴a ⇒ b
ba² ⇒ ab⁴
(ba)² ⇒ ab²ab⁹
b⁴ab²a ⇒ abab⁸⁶
a³ ⇒ 1
a(b²a)² ⇒ bab²ab⁷⁶

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, bbbb=aba〉	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, abbbb=baa〉