〈a, b | aba=b, baaab=a〉

Monoid presentation of length 10

Properties

Finite non-commutative monoid with 17 elements

Completion parameters

Reduction order: left-to-right a/b

Complete rewriting system

a⁹ ⇒ a
ba⁸ ⇒ b
ab ⇒ ba⁷
b² ⇒ a⁴

Idempotents

2 elements

1
a⁸

Cayley table

Idempotents are shown in bold.

	1	a	b	a²	ba	a³	ba²	a⁴	ba³	a⁵	ba⁴	a⁶	ba⁵	a⁷	ba⁶	a⁸	ba⁷
1	1	a	b	a²	ba	a³	ba²	a⁴	ba³	a⁵	ba⁴	a⁶	ba⁵	a⁷	ba⁶	a⁸	ba⁷
a	a	a²	ba⁷	a³	b	a⁴	ba	a⁵	ba²	a⁶	ba³	a⁷	ba⁴	a⁸	ba⁵	a	ba⁶
b	b	ba	a⁴	ba²	a⁵	ba³	a⁶	ba⁴	a⁷	ba⁵	a⁸	ba⁶	a	ba⁷	a²	b	a³
a²	a²	a³	ba⁶	a⁴	ba⁷	a⁵	b	a⁶	ba	a⁷	ba²	a⁸	ba³	a	ba⁴	a²	ba⁵
ba	ba	ba²	a³	ba³	a⁴	ba⁴	a⁵	ba⁵	a⁶	ba⁶	a⁷	ba⁷	a⁸	b	a	ba	a²
a³	a³	a⁴	ba⁵	a⁵	ba⁶	a⁶	ba⁷	a⁷	b	a⁸	ba	a	ba²	a²	ba³	a³	ba⁴
ba²	ba²	ba³	a²	ba⁴	a³	ba⁵	a⁴	ba⁶	a⁵	ba⁷	a⁶	b	a⁷	ba	a⁸	ba²	a
a⁴	a⁴	a⁵	ba⁴	a⁶	ba⁵	a⁷	ba⁶	a⁸	ba⁷	a	b	a²	ba	a³	ba²	a⁴	ba³
ba³	ba³	ba⁴	a	ba⁵	a²	ba⁶	a³	ba⁷	a⁴	b	a⁵	ba	a⁶	ba²	a⁷	ba³	a⁸
a⁵	a⁵	a⁶	ba³	a⁷	ba⁴	a⁸	ba⁵	a	ba⁶	a²	ba⁷	a³	b	a⁴	ba	a⁵	ba²
ba⁴	ba⁴	ba⁵	a⁸	ba⁶	a	ba⁷	a²	b	a³	ba	a⁴	ba²	a⁵	ba³	a⁶	ba⁴	a⁷
a⁶	a⁶	a⁷	ba²	a⁸	ba³	a	ba⁴	a²	ba⁵	a³	ba⁶	a⁴	ba⁷	a⁵	b	a⁶	ba
ba⁵	ba⁵	ba⁶	a⁷	ba⁷	a⁸	b	a	ba	a²	ba²	a³	ba³	a⁴	ba⁴	a⁵	ba⁵	a⁶
a⁷	a⁷	a⁸	ba	a	ba²	a²	ba³	a³	ba⁴	a⁴	ba⁵	a⁵	ba⁶	a⁶	ba⁷	a⁷	b
ba⁶	ba⁶	ba⁷	a⁶	b	a⁷	ba	a⁸	ba²	a	ba³	a²	ba⁴	a³	ba⁵	a⁴	ba⁶	a⁵
a⁸	a⁸	a	b	a²	ba	a³	ba²	a⁴	ba³	a⁵	ba⁴	a⁶	ba⁵	a⁷	ba⁶	a⁸	ba⁷
ba⁷	ba⁷	b	a⁵	ba	a⁶	ba²	a⁷	ba³	a⁸	ba⁴	a	ba⁵	a²	ba⁶	a³	ba⁷	a⁴

Right Cayley graph

Idempotents are shown in bold.

Left Cayley graph

Idempotents are shown in bold.

Others with same cardinality

19 unique, 71 total

Length:	Presentation:	Description:	Related:
10	〈a, b \| aaaa=b, abbbb=1〉	Isomorphic to ℤ₁₇	39 isomorphic
10	〈a, b \| aab=b, babbb=a〉	Finite non-commutative monoid with 17 elements	1 isomorphic
10	〈a, b \| aba=b, babbb=a〉	Finite non-commutative monoid with 17 elements
10	〈a, b \| bb=aa, abab=aa〉	Finite non-commutative monoid with 17 elements
10	〈a, b \| bb=aa, abab=ab〉	Finite non-commutative monoid with 17 elements
10	〈a, b \| bb=aa, abab=ba〉	Finite non-commutative monoid with 17 elements
11	〈a, b \| aab=aaa, bbb=ab〉	Finite non-commutative monoid with 17 elements
11	〈a, b \| aab=aaa, bbb=ba〉	Finite non-commutative monoid with 17 elements
11	〈a, b \| aba=aaa, baa=bb〉	Finite non-commutative monoid with 17 elements
11	〈a, b \| aba=aaa, bbb=ab〉	Finite non-commutative monoid with 17 elements
11	〈a, b \| abb=aba, bbb=aa〉	Finite non-commutative monoid with 17 elements
11	〈a, b \| aaaa=b, abbbb=a〉	Finite commutative monoid with 17 elements	2 isomorphic
11	〈a, b \| aaaa=b, abbbb=b〉	Finite commutative monoid with 17 elements	2 isomorphic
11	〈a, b \| aabb=a, baaaa=b〉	Finite non-commutative monoid with 17 elements	1 isomorphic
11	〈a, b \| abba=a, aaaab=b〉	Finite non-commutative monoid with 17 elements
11	〈a, b \| aaa=ab, babbb=b〉	Finite non-commutative monoid with 17 elements	3 isomorphic
11	〈a, b \| aab=aa, bbbb=ba〉	Finite non-commutative monoid with 17 elements
11	〈a, b \| aab=bb, bab=aaa〉	Finite non-commutative monoid with 17 elements
11	〈a, b \| aab=b, abbbba=a〉	Finite non-commutative monoid with 17 elements	4 isomorphic