〈a, b | aab=aaa, bbb=ab〉

Monoid presentation of length 11

Properties

Finite non-commutative monoid with 17 elements

Completion parameters

Reduction order: left-to-right b/a

Complete rewriting system

b⁷ ⇒ b⁶
ab ⇒ b³
b⁵a ⇒ b⁶
a³ ⇒ b⁵

Idempotents

2 elements

1
b⁶

Cayley table

Idempotents are shown in bold.

	1	a	b	a²	ba	b²	ba²	b²a	b³	b²a²	b³a	b⁴	b³a²	b⁴a	b⁵	b⁴a²	b⁶
1	1	a	b	a²	ba	b²	ba²	b²a	b³	b²a²	b³a	b⁴	b³a²	b⁴a	b⁵	b⁴a²	b⁶
a	a	a²	b³	b⁵	b³a	b⁴	b³a²	b⁴a	b⁵	b⁴a²	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶
b	b	ba	b²	ba²	b²a	b³	b²a²	b³a	b⁴	b³a²	b⁴a	b⁵	b⁴a²	b⁶	b⁶	b⁶	b⁶
a²	a²	b⁵	b⁵	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶
ba	ba	ba²	b⁴	b⁶	b⁴a	b⁵	b⁴a²	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶
b²	b²	b²a	b³	b²a²	b³a	b⁴	b³a²	b⁴a	b⁵	b⁴a²	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶
ba²	ba²	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶
b²a	b²a	b²a²	b⁵	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶
b³	b³	b³a	b⁴	b³a²	b⁴a	b⁵	b⁴a²	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶
b²a²	b²a²	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶
b³a	b³a	b³a²	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶
b⁴	b⁴	b⁴a	b⁵	b⁴a²	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶
b³a²	b³a²	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶
b⁴a	b⁴a	b⁴a²	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶
b⁵	b⁵	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶
b⁴a²	b⁴a²	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶
b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶

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=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