〈a, b | aab=aaa, bbb=ba〉

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
ba ⇒ b³
a²b³ ⇒ a²b²
a³ ⇒ a²b

Idempotents

4 elements

1
b⁶
ab⁶
a²b²

Cayley table

Idempotents are shown in bold.

	1	a	b	a²	ab	b²	a²b	ab²	b³	a²b²	ab³	b⁴	ab⁴	b⁵	ab⁵	b⁶	ab⁶
1	1	a	b	a²	ab	b²	a²b	ab²	b³	a²b²	ab³	b⁴	ab⁴	b⁵	ab⁵	b⁶	ab⁶
a	a	a²	ab	a²b	a²b	ab²	a²b²	a²b²	ab³	a²b²	a²b²	ab⁴	a²b²	ab⁵	a²b²	ab⁶	a²b²
b	b	b³	b²	b⁵	b⁴	b³	b⁶	b⁵	b⁴	b⁶	b⁶	b⁵	b⁶	b⁶	b⁶	b⁶	b⁶
a²	a²	a²b	a²b	a²b²	a²b²	a²b²	a²b²	a²b²	a²b²	a²b²	a²b²	a²b²	a²b²	a²b²	a²b²	a²b²	a²b²
ab	ab	ab³	ab²	ab⁵	ab⁴	ab³	ab⁶	ab⁵	ab⁴	ab⁶	ab⁶	ab⁵	ab⁶	ab⁶	ab⁶	ab⁶	ab⁶
b²	b²	b⁴	b³	b⁶	b⁵	b⁴	b⁶	b⁶	b⁵	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶
a²b	a²b	a²b²	a²b²	a²b²	a²b²	a²b²	a²b²	a²b²	a²b²	a²b²	a²b²	a²b²	a²b²	a²b²	a²b²	a²b²	a²b²
ab²	ab²	ab⁴	ab³	ab⁶	ab⁵	ab⁴	ab⁶	ab⁶	ab⁵	ab⁶	ab⁶	ab⁶	ab⁶	ab⁶	ab⁶	ab⁶	ab⁶
b³	b³	b⁵	b⁴	b⁶	b⁶	b⁵	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶
a²b²	a²b²	a²b²	a²b²	a²b²	a²b²	a²b²	a²b²	a²b²	a²b²	a²b²	a²b²	a²b²	a²b²	a²b²	a²b²	a²b²	a²b²
ab³	ab³	ab⁵	ab⁴	ab⁶	ab⁶	ab⁵	ab⁶	ab⁶	ab⁶	ab⁶	ab⁶	ab⁶	ab⁶	ab⁶	ab⁶	ab⁶	ab⁶
b⁴	b⁴	b⁶	b⁵	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶
ab⁴	ab⁴	ab⁶	ab⁵	ab⁶	ab⁶	ab⁶	ab⁶	ab⁶	ab⁶	ab⁶	ab⁶	ab⁶	ab⁶	ab⁶	ab⁶	ab⁶	ab⁶
b⁵	b⁵	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶
ab⁵	ab⁵	ab⁶	ab⁶	ab⁶	ab⁶	ab⁶	ab⁶	ab⁶	ab⁶	ab⁶	ab⁶	ab⁶	ab⁶	ab⁶	ab⁶	ab⁶	ab⁶
b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶	b⁶
ab⁶	ab⁶	ab⁶	ab⁶	ab⁶	ab⁶	ab⁶	ab⁶	ab⁶	ab⁶	ab⁶	ab⁶	ab⁶	ab⁶	ab⁶	ab⁶	ab⁶	ab⁶

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 \| 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