〈a, b | aba=b, babbb=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

a⁵ ⇒ a
ba⁴ ⇒ b
ab ⇒ ba³
b⁴ ⇒ a²

Idempotents

2 elements

1
a⁴

Cayley table

Idempotents are shown in bold.

	1	a	b	a²	ba	b²	a³	ba²	b²a	b³	a⁴	ba³	b²a²	b³a	b²a³	b³a²	b³a³
1	1	a	b	a²	ba	b²	a³	ba²	b²a	b³	a⁴	ba³	b²a²	b³a	b²a³	b³a²	b³a³
a	a	a²	ba³	a³	b	b²a	a⁴	ba	b²a²	b³a³	a	ba²	b²a³	b³	b²	b³a	b³a²
b	b	ba	b²	ba²	b²a	b³	ba³	b²a²	b³a	a²	b	b²a³	b³a²	a³	b³a³	a⁴	a
a²	a²	a³	ba²	a⁴	ba³	b²a²	a	b	b²a³	b³a²	a²	ba	b²	b³a³	b²a	b³	b³a
ba	ba	ba²	b²a³	ba³	b²	b³a	b	b²a	b³a²	a	ba	b²a²	b³a³	a²	b³	a³	a⁴
b²	b²	b²a	b³	b²a²	b³a	a²	b²a³	b³a²	a³	ba²	b²	b³a³	a⁴	ba³	a	b	ba
a³	a³	a⁴	ba	a	ba²	b²a³	a²	ba³	b²	b³a	a³	b	b²a	b³a²	b²a²	b³a³	b³
ba²	ba²	ba³	b²a²	b	b²a³	b³a²	ba	b²	b³a³	a⁴	ba²	b²a	b³	a	b³a	a²	a³
b²a	b²a	b²a²	b³a³	b²a³	b³	a³	b²	b³a	a⁴	ba	b²a	b³a²	a	ba²	a²	ba³	b
b³	b³	b³a	a²	b³a²	a³	ba²	b³a³	a⁴	ba³	b²a²	b³	a	b	b²a³	ba	b²	b²a
a⁴	a⁴	a	b	a²	ba	b²	a³	ba²	b²a	b³	a⁴	ba³	b²a²	b³a	b²a³	b³a²	b³a³
ba³	ba³	b	b²a	ba	b²a²	b³a³	ba²	b²a³	b³	a³	ba³	b²	b³a	a⁴	b³a²	a	a²
b²a²	b²a²	b²a³	b³a²	b²	b³a³	a⁴	b²a	b³	a	b	b²a²	b³a	a²	ba	a³	ba²	ba³
b³a	b³a	b³a²	a	b³a³	a²	ba³	b³	a³	b	b²a	b³a	a⁴	ba	b²a²	ba²	b²a³	b²
b²a³	b²a³	b²	b³a	b²a	b³a²	a	b²a²	b³a³	a²	ba³	b²a³	b³	a³	b	a⁴	ba	ba²
b³a²	b³a²	b³a³	a⁴	b³	a	b	b³a	a²	ba	b²	b³a²	a³	ba²	b²a	ba³	b²a²	b²a³
b³a³	b³a³	b³	a³	b³a	a⁴	ba	b³a²	a	ba²	b²a³	b³a³	a²	ba³	b²	b	b²a	b²a²

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, baaab=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