〈a, b | aab=bb, bab=aaa〉

Monoid presentation of length 11

Properties

Finite non-commutative monoid with 17 elements

Completion parameters

Reduction order: left-to-right a/b

Complete rewriting system

a⁸ ⇒ a⁶
ba³ ⇒ a⁵
a³b ⇒ a⁷
b² ⇒ a²b
bab ⇒ a³
ba²b ⇒ a⁶

Idempotents

2 elements

1
a⁶

Cayley table

Idempotents are shown in bold.

	1	a	b	a²	ab	ba	a³	a²b	aba	ba²	a⁴	a²ba	aba²	a⁵	a²ba²	a⁶	a⁷
1	1	a	b	a²	ab	ba	a³	a²b	aba	ba²	a⁴	a²ba	aba²	a⁵	a²ba²	a⁶	a⁷
a	a	a²	ab	a³	a²b	aba	a⁴	a⁷	a²ba	aba²	a⁵	a⁶	a²ba²	a⁶	a⁷	a⁷	a⁶
b	b	ba	a²b	ba²	a³	a²ba	a⁵	a⁶	a⁴	a²ba²	a⁶	a⁷	a⁵	a⁷	a⁶	a⁶	a⁷
a²	a²	a³	a²b	a⁴	a⁷	a²ba	a⁵	a⁶	a⁶	a²ba²	a⁶	a⁷	a⁷	a⁷	a⁶	a⁶	a⁷
ab	ab	aba	a⁷	aba²	a⁴	a⁶	a⁶	a⁷	a⁵	a⁷	a⁷	a⁶	a⁶	a⁶	a⁷	a⁷	a⁶
ba	ba	ba²	a³	a⁵	a⁶	a⁴	a⁶	a⁷	a⁷	a⁵	a⁷	a⁶	a⁶	a⁶	a⁷	a⁷	a⁶
a³	a³	a⁴	a⁷	a⁵	a⁶	a⁶	a⁶	a⁷	a⁷	a⁷	a⁷	a⁶	a⁶	a⁶	a⁷	a⁷	a⁶
a²b	a²b	a²ba	a⁶	a²ba²	a⁵	a⁷	a⁷	a⁶	a⁶	a⁶	a⁶	a⁷	a⁷	a⁷	a⁶	a⁶	a⁷
aba	aba	aba²	a⁴	a⁶	a⁷	a⁵	a⁷	a⁶	a⁶	a⁶	a⁶	a⁷	a⁷	a⁷	a⁶	a⁶	a⁷
ba²	ba²	a⁵	a⁶	a⁶	a⁷	a⁷	a⁷	a⁶	a⁶	a⁶	a⁶	a⁷	a⁷	a⁷	a⁶	a⁶	a⁷
a⁴	a⁴	a⁵	a⁶	a⁶	a⁷	a⁷	a⁷	a⁶	a⁶	a⁶	a⁶	a⁷	a⁷	a⁷	a⁶	a⁶	a⁷
a²ba	a²ba	a²ba²	a⁵	a⁷	a⁶	a⁶	a⁶	a⁷	a⁷	a⁷	a⁷	a⁶	a⁶	a⁶	a⁷	a⁷	a⁶
aba²	aba²	a⁶	a⁷	a⁷	a⁶	a⁶	a⁶	a⁷	a⁷	a⁷	a⁷	a⁶	a⁶	a⁶	a⁷	a⁷	a⁶
a⁵	a⁵	a⁶	a⁷	a⁷	a⁶	a⁶	a⁶	a⁷	a⁷	a⁷	a⁷	a⁶	a⁶	a⁶	a⁷	a⁷	a⁶
a²ba²	a²ba²	a⁷	a⁶	a⁶	a⁷	a⁷	a⁷	a⁶	a⁶	a⁶	a⁶	a⁷	a⁷	a⁷	a⁶	a⁶	a⁷
a⁶	a⁶	a⁷	a⁶	a⁶	a⁷	a⁷	a⁷	a⁶	a⁶	a⁶	a⁶	a⁷	a⁷	a⁷	a⁶	a⁶	a⁷
a⁷	a⁷	a⁶	a⁷	a⁷	a⁶	a⁶	a⁶	a⁷	a⁷	a⁷	a⁷	a⁶	a⁶	a⁶	a⁷	a⁷	a⁶

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 \| 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=b, abbbba=a〉	Finite non-commutative monoid with 17 elements	4 isomorphic