〈a, b | aab=b, babbb=a〉

Monoid presentation of length 10

Properties

Finite non-commutative monoid with 17 elements

Completion parameters

Reduction order: left-to-right b/a

Complete rewriting system

b⁹ ⇒ b
ab⁸ ⇒ a
ba ⇒ ab⁵
a² ⇒ b⁸

Idempotents

2 elements

1
b⁸

Cayley table

Idempotents are shown in bold.

	1	a	b	ab	b²	ab²	b³	ab³	b⁴	ab⁴	b⁵	ab⁵	b⁶	ab⁶	b⁷	ab⁷	b⁸
1	1	a	b	ab	b²	ab²	b³	ab³	b⁴	ab⁴	b⁵	ab⁵	b⁶	ab⁶	b⁷	ab⁷	b⁸
a	a	b⁸	ab	b	ab²	b²	ab³	b³	ab⁴	b⁴	ab⁵	b⁵	ab⁶	b⁶	ab⁷	b⁷	a
b	b	ab⁵	b²	ab⁶	b³	ab⁷	b⁴	a	b⁵	ab	b⁶	ab²	b⁷	ab³	b⁸	ab⁴	b
ab	ab	b⁵	ab²	b⁶	ab³	b⁷	ab⁴	b⁸	ab⁵	b	ab⁶	b²	ab⁷	b³	a	b⁴	ab
b²	b²	ab²	b³	ab³	b⁴	ab⁴	b⁵	ab⁵	b⁶	ab⁶	b⁷	ab⁷	b⁸	a	b	ab	b²
ab²	ab²	b²	ab³	b³	ab⁴	b⁴	ab⁵	b⁵	ab⁶	b⁶	ab⁷	b⁷	a	b⁸	ab	b	ab²
b³	b³	ab⁷	b⁴	a	b⁵	ab	b⁶	ab²	b⁷	ab³	b⁸	ab⁴	b	ab⁵	b²	ab⁶	b³
ab³	ab³	b⁷	ab⁴	b⁸	ab⁵	b	ab⁶	b²	ab⁷	b³	a	b⁴	ab	b⁵	ab²	b⁶	ab³
b⁴	b⁴	ab⁴	b⁵	ab⁵	b⁶	ab⁶	b⁷	ab⁷	b⁸	a	b	ab	b²	ab²	b³	ab³	b⁴
ab⁴	ab⁴	b⁴	ab⁵	b⁵	ab⁶	b⁶	ab⁷	b⁷	a	b⁸	ab	b	ab²	b²	ab³	b³	ab⁴
b⁵	b⁵	ab	b⁶	ab²	b⁷	ab³	b⁸	ab⁴	b	ab⁵	b²	ab⁶	b³	ab⁷	b⁴	a	b⁵
ab⁵	ab⁵	b	ab⁶	b²	ab⁷	b³	a	b⁴	ab	b⁵	ab²	b⁶	ab³	b⁷	ab⁴	b⁸	ab⁵
b⁶	b⁶	ab⁶	b⁷	ab⁷	b⁸	a	b	ab	b²	ab²	b³	ab³	b⁴	ab⁴	b⁵	ab⁵	b⁶
ab⁶	ab⁶	b⁶	ab⁷	b⁷	a	b⁸	ab	b	ab²	b²	ab³	b³	ab⁴	b⁴	ab⁵	b⁵	ab⁶
b⁷	b⁷	ab³	b⁸	ab⁴	b	ab⁵	b²	ab⁶	b³	ab⁷	b⁴	a	b⁵	ab	b⁶	ab²	b⁷
ab⁷	ab⁷	b³	a	b⁴	ab	b⁵	ab²	b⁶	ab³	b⁷	ab⁴	b⁸	ab⁵	b	ab⁶	b²	ab⁷
b⁸	b⁸	a	b	ab	b²	ab²	b³	ab³	b⁴	ab⁴	b⁵	ab⁵	b⁶	ab⁶	b⁷	ab⁷	b⁸

Right Cayley graph

Idempotents are shown in bold.

Left Cayley graph

Idempotents are shown in bold.

Others with same cardinality

19 unique, 70 total

Length:	Presentation:	Description:	Related:
10	〈a, b \| aaaa=b, abbbb=1〉	Isomorphic to ℤ₁₇	39 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=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

Other isomorphic instances

1 total

Length:	Presentation:
10	〈a, b \| aab=b, bbbab=a〉