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〈a, b | aba=b, baab=aaa〉

Monoid presentation of length 11

Properties

Finite non-commutative monoid with 23 elements

Completion parameters

Reduction order: left-to-right a/b

Complete rewriting system

a¹³ ⇒ a³
ba¹⁰ ⇒ b
ab ⇒ ba⁹
b² ⇒ a⁵

Idempotents

2 elements

1
a¹⁰

Cayley table

Idempotents are shown in bold.

	1	a	b	a²	ba	a³	ba²	a⁴	ba³	a⁵	ba⁴	a⁶	ba⁵	a⁷	ba⁶	a⁸	ba⁷	a⁹	ba⁸	a¹⁰	ba⁹	a¹¹	a¹²
1	1	a	b	a²	ba	a³	ba²	a⁴	ba³	a⁵	ba⁴	a⁶	ba⁵	a⁷	ba⁶	a⁸	ba⁷	a⁹	ba⁸	a¹⁰	ba⁹	a¹¹	a¹²
a	a	a²	ba⁹	a³	b	a⁴	ba	a⁵	ba²	a⁶	ba³	a⁷	ba⁴	a⁸	ba⁵	a⁹	ba⁶	a¹⁰	ba⁷	a¹¹	ba⁸	a¹²	a³
b	b	ba	a⁵	ba²	a⁶	ba³	a⁷	ba⁴	a⁸	ba⁵	a⁹	ba⁶	a¹⁰	ba⁷	a¹¹	ba⁸	a¹²	ba⁹	a³	b	a⁴	ba	ba²
a²	a²	a³	ba⁸	a⁴	ba⁹	a⁵	b	a⁶	ba	a⁷	ba²	a⁸	ba³	a⁹	ba⁴	a¹⁰	ba⁵	a¹¹	ba⁶	a¹²	ba⁷	a³	a⁴
ba	ba	ba²	a⁴	ba³	a⁵	ba⁴	a⁶	ba⁵	a⁷	ba⁶	a⁸	ba⁷	a⁹	ba⁸	a¹⁰	ba⁹	a¹¹	b	a¹²	ba	a³	ba²	ba³
a³	a³	a⁴	ba⁷	a⁵	ba⁸	a⁶	ba⁹	a⁷	b	a⁸	ba	a⁹	ba²	a¹⁰	ba³	a¹¹	ba⁴	a¹²	ba⁵	a³	ba⁶	a⁴	a⁵
ba²	ba²	ba³	a³	ba⁴	a⁴	ba⁵	a⁵	ba⁶	a⁶	ba⁷	a⁷	ba⁸	a⁸	ba⁹	a⁹	b	a¹⁰	ba	a¹¹	ba²	a¹²	ba³	ba⁴
a⁴	a⁴	a⁵	ba⁶	a⁶	ba⁷	a⁷	ba⁸	a⁸	ba⁹	a⁹	b	a¹⁰	ba	a¹¹	ba²	a¹²	ba³	a³	ba⁴	a⁴	ba⁵	a⁵	a⁶
ba³	ba³	ba⁴	a¹²	ba⁵	a³	ba⁶	a⁴	ba⁷	a⁵	ba⁸	a⁶	ba⁹	a⁷	b	a⁸	ba	a⁹	ba²	a¹⁰	ba³	a¹¹	ba⁴	ba⁵
a⁵	a⁵	a⁶	ba⁵	a⁷	ba⁶	a⁸	ba⁷	a⁹	ba⁸	a¹⁰	ba⁹	a¹¹	b	a¹²	ba	a³	ba²	a⁴	ba³	a⁵	ba⁴	a⁶	a⁷
ba⁴	ba⁴	ba⁵	a¹¹	ba⁶	a¹²	ba⁷	a³	ba⁸	a⁴	ba⁹	a⁵	b	a⁶	ba	a⁷	ba²	a⁸	ba³	a⁹	ba⁴	a¹⁰	ba⁵	ba⁶
a⁶	a⁶	a⁷	ba⁴	a⁸	ba⁵	a⁹	ba⁶	a¹⁰	ba⁷	a¹¹	ba⁸	a¹²	ba⁹	a³	b	a⁴	ba	a⁵	ba²	a⁶	ba³	a⁷	a⁸
ba⁵	ba⁵	ba⁶	a¹⁰	ba⁷	a¹¹	ba⁸	a¹²	ba⁹	a³	b	a⁴	ba	a⁵	ba²	a⁶	ba³	a⁷	ba⁴	a⁸	ba⁵	a⁹	ba⁶	ba⁷
a⁷	a⁷	a⁸	ba³	a⁹	ba⁴	a¹⁰	ba⁵	a¹¹	ba⁶	a¹²	ba⁷	a³	ba⁸	a⁴	ba⁹	a⁵	b	a⁶	ba	a⁷	ba²	a⁸	a⁹
ba⁶	ba⁶	ba⁷	a⁹	ba⁸	a¹⁰	ba⁹	a¹¹	b	a¹²	ba	a³	ba²	a⁴	ba³	a⁵	ba⁴	a⁶	ba⁵	a⁷	ba⁶	a⁸	ba⁷	ba⁸
a⁸	a⁸	a⁹	ba²	a¹⁰	ba³	a¹¹	ba⁴	a¹²	ba⁵	a³	ba⁶	a⁴	ba⁷	a⁵	ba⁸	a⁶	ba⁹	a⁷	b	a⁸	ba	a⁹	a¹⁰
ba⁷	ba⁷	ba⁸	a⁸	ba⁹	a⁹	b	a¹⁰	ba	a¹¹	ba²	a¹²	ba³	a³	ba⁴	a⁴	ba⁵	a⁵	ba⁶	a⁶	ba⁷	a⁷	ba⁸	ba⁹
a⁹	a⁹	a¹⁰	ba	a¹¹	ba²	a¹²	ba³	a³	ba⁴	a⁴	ba⁵	a⁵	ba⁶	a⁶	ba⁷	a⁷	ba⁸	a⁸	ba⁹	a⁹	b	a¹⁰	a¹¹
ba⁸	ba⁸	ba⁹	a⁷	b	a⁸	ba	a⁹	ba²	a¹⁰	ba³	a¹¹	ba⁴	a¹²	ba⁵	a³	ba⁶	a⁴	ba⁷	a⁵	ba⁸	a⁶	ba⁹	b
a¹⁰	a¹⁰	a¹¹	b	a¹²	ba	a³	ba²	a⁴	ba³	a⁵	ba⁴	a⁶	ba⁵	a⁷	ba⁶	a⁸	ba⁷	a⁹	ba⁸	a¹⁰	ba⁹	a¹¹	a¹²
ba⁹	ba⁹	b	a⁶	ba	a⁷	ba²	a⁸	ba³	a⁹	ba⁴	a¹⁰	ba⁵	a¹¹	ba⁶	a¹²	ba⁷	a³	ba⁸	a⁴	ba⁹	a⁵	b	ba
a¹¹	a¹¹	a¹²	ba⁹	a³	b	a⁴	ba	a⁵	ba²	a⁶	ba³	a⁷	ba⁴	a⁸	ba⁵	a⁹	ba⁶	a¹⁰	ba⁷	a¹¹	ba⁸	a¹²	a³
a¹²	a¹²	a³	ba⁸	a⁴	ba⁹	a⁵	b	a⁶	ba	a⁷	ba²	a⁸	ba³	a⁹	ba⁴	a¹⁰	ba⁵	a¹¹	ba⁶	a¹²	ba⁷	a³	a⁴

Right Cayley graph

Idempotents are shown in bold.

Left Cayley graph

Idempotents are shown in bold.

Others with same cardinality

1 unique, 1 total

Length:	Presentation:	Description:	Related:
11	〈a, b \| aaa=a, ababba=b〉	Finite non-commutative monoid with 23 elements