〈a, b | aba=bb, aaaaa=1〉

Monoid presentation of length 10

Properties

Finite non-commutative monoid with 605 elements

Completion parameters

Reduction order: left-to-right b/a

Complete rewriting system

b³¹ ⇒ b
bab³⁰ ⇒ ba
b³a ⇒ ab³
aba ⇒ b²
ba²b³⁰ ⇒ ba²
a³b ⇒ bab²ab²⁶
a(b²a)² ⇒ b²a²b⁵
ba³ ⇒ (b²a)²b²⁵
b(ab²a)² ⇒ a²b²a²b⁸
(b²a²)² ⇒ (ab²a)²b²⁵
a⁵ ⇒ 1
b(a²b²)²a ⇒ (a²b²)²ab¹¹

Idempotents

2 elements

1
b³⁰

Right Cayley graph

Left Cayley graph

Others with same cardinality

3 unique, 3 total

Length:	Presentation:	Description:	Related:
10	〈a, b \| abba=b, aaaaa=1〉	Finite non-commutative monoid with 605 elements
11	〈a, b \| babab=a, bbbbb=1〉	Finite non-commutative monoid with 605 elements
11	〈a, b \| bab=aba, aaaaa=1〉	Finite non-commutative monoid with 605 elements