〈a, b | aaa=1, abbba=b〉

Monoid presentation of length 9

Properties

Finite non-commutative monoid with 147 elements

Completion parameters

Reduction order: left-to-right b/a

Complete rewriting system

b²⁵ ⇒ b
bab²⁴ ⇒ ba
b⁴a ⇒ ab⁴
a²b ⇒ b³a
ab²a ⇒ bab²¹
ab³a ⇒ b
ba² ⇒ ab³
(ba)² ⇒ abab⁷
a³ ⇒ 1

Idempotents

2 elements

1
b²⁴

Right Cayley graph

Left Cayley graph

Others with same cardinality

3 unique, 6 total

Length:	Presentation:	Description:	Related:
9	〈a, b \| bab=aaa, bbb=1〉	Finite non-commutative monoid with 147 elements	3 isomorphic
11	〈a, b \| aaa=1, abababa=b〉	Finite non-commutative monoid with 147 elements
11	〈a, b \| aaa=1, babab=aba〉	Finite non-commutative monoid with 147 elements

Other isomorphic instances

3 total

Length:	Presentation:
10	〈a, b \| aaa=1, abbb=baa〉
11	〈a, b \| aaa=1, aabbba=ab〉
11	〈a, b \| aaa=1, aabaa=bbb〉