〈a, b | bab=aaa, bbb=1〉

Monoid presentation of length 9

Properties

Finite non-commutative monoid with 147 elements

Completion parameters

Reduction order: left-to-right a/b

Complete rewriting system

a²⁵ ⇒ a
aba²⁴ ⇒ ab
a⁴b ⇒ ba⁴
b²a ⇒ aba²²
bab ⇒ a³
ba²b ⇒ a³ba³
ab² ⇒ a²ba²¹
aba³b ⇒ ba³ba⁷
b³ ⇒ 1

Idempotents

2 elements

1
a²⁴

Right Cayley graph

Left Cayley graph

Others with same cardinality

3 unique, 6 total

Length:	Presentation:	Description:	Related:
9	〈a, b \| aaa=1, abbba=b〉	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, aabbb=ba〉
11	〈a, b \| aaa=1, aabbbaa=b〉
11	〈a, b \| aaa=1, abbb=aaba〉